# zbMATH — the first resource for mathematics

## Murota, Kazuo

Compute Distance To:
 Author ID: murota.kazuo Published as: Murota, K.; Murota, Kazuo Homepage: http://www.comp.tmu.ac.jp/kzmurota/index.en.html External Links: MGP · Wikidata · ORCID · dblp · GND
 Documents Indexed: 190 Publications since 1980, including 8 Books
all top 5

#### Co-Authors

 56 single-authored 20 Ikeda, Kiyohiro 20 Shioura, Akiyoshi 12 Sugihara, Masaaki 12 Tamura, Akihisa 11 Iwata, Satoru 10 Iri, Masao 10 Moriguchi, Satoko 8 Maehara, Takanori 7 Aishima, Kensuke 7 Matsuo, Takayasu 5 Hirai, Hiroshi 5 Kojima, Masakazu 5 Tanaka, Ken’ichiro 4 Fukuda, Mituhiro 4 Kobayashi, Yusuke 4 Nakata, Kazuhide 3 Fujisawa, Katsuki 3 Fujishige, Satoru 3 Iwamasa, Yuni 3 Kanno, Yoshihiro 3 Tardella, Fabio 3 Živný, Stanislav 2 Akamatsu, Takashi 2 Iimura, Takuya 2 Katoh, Naoki 2 Marumo, Naoki 2 Matsui, Shouichi 2 Ohsaki, Makoto 2 Ohya, Takao 2 Rikitoku, Masaki 2 Saito, Hiroo 2 Sakuta, Izumi 2 Tanaka, Reiko J. 2 Van der Woude, Jacob Willem 2 Weismantel, Robert 2 Yang, Zaifu 1 Aiura, Daishi 1 Aoki, Satoshi 1 Bolandnazar, Mohammadreza 1 Danilov, Vladimir I. 1 Elishakoff, Isaac 1 Fujii, Hiroshi 1 Geelen, James F. 1 Harvey, Nicholas J. A. 1 Huh, Woonghee Tim 1 Imai, Hideki 1 Ito, Hisashi 1 Ito, Shinji 1 Kakimura, Naonori 1 Karger, David R. 1 Kojima, Sadayoshi 1 Koshevoy, Gleb A. 1 Kubota, Koichi 1 Maruyama, Kiyoshi 1 McCormick, S. Thomas 1 Mori, Masatake 1 Nakamura, Masataka 1 Nakano, Masaki 1 Noguchi, Hirohisa 1 Otsuki, Kensuke 1 Poljak, Svatopluk 1 Saiki, Isao 1 Scharbrodt, Mark 1 Shigeno, Maiko 1 Suzuki, Taiji 1 Takayama, Yuki 1 Takeuchi, Kei 1 Terada, Kenjiro 1 Yanagimoto, Akito 1 Yasunami, H. 1 Yokoi, Yu
all top 5

#### Serials

 14 Japan Journal of Industrial and Applied Mathematics 14 Mathematical Programming. Series A. Series B 13 Discrete Applied Mathematics 11 RIMS Kokyuroku 10 Journal of the Operations Research Society of Japan 9 SIAM Journal on Matrix Analysis and Applications 7 Linear Algebra and its Applications 6 Mathematics of Operations Research 5 International Journal of Solids and Structures 5 SIAM Journal on Discrete Mathematics 3 Computer Methods in Applied Mechanics and Engineering 3 Mathematics of Computation 3 Journal of Computational and Applied Mathematics 3 SIAM Journal on Computing 3 SIAM Journal on Control and Optimization 3 Advances in Applied Mathematics 3 Discrete Optimization 3 Algorithms and Combinatorics 3 Applied Mathematical Sciences 2 Computers and Structures 2 Advances in Mathematics 2 Journal of Combinatorial Theory. Series B 2 Numerische Mathematik 2 Operations Research Letters 2 Combinatorica 2 Applied Mathematics Letters 2 SIAM Journal on Applied Mathematics 2 SIAM Journal on Optimization 2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2 Optimization Methods & Software 2 Pacific Journal of Optimization 1 International Journal of Control 1 Information Processing Letters 1 Linear and Multilinear Algebra 1 Biometrika 1 IEEE Transactions on Automatic Control 1 Journal of Mathematical Economics 1 Networks 1 Operations Research 1 SIAM Journal on Numerical Analysis 1 Utilitas Mathematica 1 SIAM Journal on Scientific and Statistical Computing 1 Mathematical Social Sciences 1 SIAM Journal on Algebraic and Discrete Methods 1 Japan Journal of Applied Mathematics 1 Annals of Operations Research 1 YUJOR. Yugoslav Journal of Operations Research 1 European Journal of Operational Research 1 Applicable Algebra in Engineering, Communication and Computing 1 SIAM Journal on Scientific Computing 1 Optimization and Engineering 1 SIAM Monographs on Discrete Mathematics and Applications 1 Optimization Letters 1 RIMS Kôkyûroku Bessatsu 1 International Journal of Economic Theory 1 Journal of Math-for-Industry 1 ACM Transactions on Algorithms 1 JSIAM Letters
all top 5

#### Fields

 93 Operations research, mathematical programming (90-XX) 57 Combinatorics (05-XX) 36 Numerical analysis (65-XX) 30 Linear and multilinear algebra; matrix theory (15-XX) 19 Computer science (68-XX) 16 Systems theory; control (93-XX) 15 Mechanics of deformable solids (74-XX) 13 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 12 Convex and discrete geometry (52-XX) 7 Statistics (62-XX) 6 Approximations and expansions (41-XX) 5 Information and communication theory, circuits (94-XX) 3 Ordinary differential equations (34-XX) 3 Dynamical systems and ergodic theory (37-XX) 2 Group theory and generalizations (20-XX) 2 Real functions (26-XX) 2 Functions of a complex variable (30-XX) 2 Partial differential equations (35-XX) 2 Probability theory and stochastic processes (60-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Special functions (33-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Geometry (51-XX) 1 Global analysis, analysis on manifolds (58-XX)

#### Citations contained in zbMATH

155 Publications have been cited 1,523 times in 750 Documents Cited by Year
Discrete convex analysis. Zbl 1029.90055
Murota, Kazuo
2003
Matrices and matroids for systems analysis. Zbl 0948.05001
Murota, Kazuo
2000
Discrete convex analysis. Zbl 0920.90103
Murota, Kazuo
1998
Systems analysis by graphs and matroids. Structural solvability and controllability. Zbl 0624.05001
Murota, Kazuo
1987
Convexity and Steinitz’s exchange property. Zbl 0867.90092
Murota, Kazuo
1996
$$M$$-convex function on generalized polymatroid. Zbl 0977.90044
Murota, Kazuo; Shioura, Akiyoshi
1999
Exploiting sparsity in semidefinite programming via matrix completion. I: General framework. Zbl 1010.90053
Fukuda, Mituhiro; Kojima, Masakazu; Murota, Kazuo; Nakata, Kazuhide
2000
Voronoi diagram in the Laguerre geometry and its applications. Zbl 0556.68038
Imai, Hiroshi; Iri, Masao; Murota, Kazuo
1985
Notes on L-/M-convex functions and the separation theorems. Zbl 0974.90019
Fujishige, Satoru; Murota, Kazuo
2000
Improvements of the incremental method for the Voronoi diagram with computational comparison of various algorithms. Zbl 0556.68039
Ohya, Takao; Iri, Masao; Murota, Kazuo
1984
Exploiting sparsity in semidefinite programming via matrix completion. II: Implementation and numerical results. Zbl 1030.90081
Nakata, Kazuhide; Fujisawa, Katsuki; Fukuda, Mituhiro; Kojima, Masakazu; Murota, Kazuo
2003
Discrete convexity and equilibria in economies with indivisible goods and money. Zbl 1004.91052
Danilov, Vladimir; Koshevoy, Gleb; Murota, Kazuo
2001
Recent developments in discrete convex analysis. Zbl 1359.05020
Murota, Kazuo
2009
Valuated matroid intersection. I: Optimality criteria. Zbl 0868.90132
Murota, Kazuo
1996
Valuated matroid intersection. II: Algorithms. Zbl 0868.90133
Murota, Kazuo
1996
Function classes for successful DE-sinc approximations. Zbl 1198.65037
Tanaka, Ken’ichiro; Sugihara, Masaaki; Murota, Kazuo
2009
Group symmetry in interior-point methods for semidefinite program. Zbl 1035.90056
Kanno, Yoshihiro; Ohsaki, Makoto; Murota, Kazuo; Katoh, Naoki
2001
Relationship of M-/L-convex functions with discrete convex functions by Miller and Favati-Tardella. Zbl 1076.90036
Murota, Kazuo; Shioura, Akiyoshi
2001
Bifurcation hierarchy of symmetric structures. Zbl 0762.73058
Ikeda, Kiyohiro; Murota, Kazuo; Fujii, Hiroshi
1991
The studentized empirical characteristic function and its application to test for the shape of distribution. Zbl 0463.62041
Murota, Kazuo; Takeuchi, Kei
1981
Extension of M-convexity and L-convexity to polyhedral convex functions. Zbl 1073.90544
Murota, Kazuo; Shioura, Akiyoshi
2000
$$M$$-convex functions on jump systems: a general framework for minsquare graph factor problem. Zbl 1119.90031
Murota, Kazuo
2006
Discrete fixed point theorem reconsidered. Zbl 1119.58006
Iimura, Takuya; Murota, Kazuo; Tamura, Akihisa
2005
Comparison of conventional and “invariant” schemes of fundamental solutions method for annular domains. Zbl 0831.65118
Murota, Kazuo
1995
A fast Voronoi-diagram algorithm with applications to geographical optimization problems. Zbl 0557.90025
Iri, Masao; Murota, Kazuo; Ohya, Takao
1984
A numerical algorithm for block-diagonal decomposition of matrix $$*$$-algebras with application to semidefinite programming. Zbl 1204.65068
Murota, Kazuo; Kanno, Yoshihiro; Kojima, Masakazu; Kojima, Sadayoshi
2010
Function classes for double exponential integration formulas. Zbl 1162.65014
Tanaka, Ken’ichiro; Sugihara, Masaaki; Murota, Kazuo; Mori, Masatake
2009
New characterizations of M-convex functions and their applications to economic equilibrium models with indivisibilities. Zbl 1094.90023
Murota, Kazuo; Tamura, Akihisa
2003
On circuit valuation of matroids. Zbl 0979.05028
Murota, Kazuo; Tamura, Akihisa
2001
Submodular flow problem with a nonseparable cost function. Zbl 0947.90119
Murota, Kazuo
1999
Computational use of group theory in bifurcation analysis of symmetric structures. Zbl 0721.65029
Murota, Kazuo; Ikeda, Kiyohiro
1991
Computing the degree of determinants via combinatorial relaxation. Zbl 0834.05037
Murota, Kazuo
1995
Finding optimal minors of valuated bimatroids. Zbl 0833.05017
Murota, K.
1995
Bifurcation analysis of symmetric structures using block-diagonalization. Zbl 0764.73100
Ikeda, Kiyohiro; Murota, Kazuo
1991
Combinatorial canonical form of layered mixed matrices and its application to block-triangularization of systems of linear/nonlinear equations. Zbl 0623.65033
Murota, Kazuo; Iri, Masao; Nakamura, Masataka
1987
Note on multimodularity and L-convexity. Zbl 1082.90071
Murota, Kazuo
2005
$$M$$-convex functions and tree metrics. Zbl 1084.90036
Hirai, Hiroshi; Murota, Kazuo
2004
Critical initial imperfection of structures. Zbl 0721.73021
Ikeda, Kiyohiro; Murota, Kazuo
1990
Computing Puiseux-series solutions to determinantal equations via combinatorial relaxation. Zbl 0711.68066
Murota, Kazuo
1990
Matrices and matroids for systems analysis. 2nd printing. Zbl 1181.05001
Murota, Kazuo
2010
Deterministic network coding by matrix completion. Zbl 1297.68022
Harvey, Nicholas J. A.; Karger, David R.; Murota, Kazuo
2005
Imperfect bifurcation in structures and materials. Engineering use of group-theoretic bifucation theory. Zbl 1005.74001
Ikeda, Kiyohiro; Murota, Kazuo
2002
Combinatorial relaxation algorithm for the maximum degree of subdeterminants: Computing Smith-McMillan form at infinity and structural indices in Kronecker form. Zbl 0826.05044
Murota, Kazuo
1995
Structural solvability of systems of equations. A mathematical formulation for distinguishing accurate and inaccurate numbers in structural analysis of systems. Zbl 0598.15003
Murota, Kazuo; Iri, Masao
1985
Imperfect bifurcation in structures and materials. Engineering use of group-theoretic bifurcation theory. 2nd ed. Zbl 1204.74003
Ikeda, Kiyohiro; Murota, Kazuo
2010
Complex analytic approach to the sinc-Gauss sampling formula. Zbl 1152.65123
Tanaka, Ken’ichiro; Sugihara, Masaaki; Murota, Kazuo
2008
Operations on M-convex functions on jump systems. Zbl 1144.90015
Kobayashi, Yusuke; Murota, Kazuo; Tanaka, Ken’ichiro
2007
On steepest descent algorithms for discrete convex functions. Zbl 1071.90027
Murota, Kazuo
2003
Application of M-convex submodular flow problem to mathematical economics. Zbl 1092.91058
Murota, Kazuo; Tamura, Akihisa
2003
Matroid valuation on independent sets. Zbl 0867.05017
Murota, Kazuo
1997
Parameter tuning and repeated application of the IMT-type transformation in numerical quadrature. Zbl 0478.65010
Murota, Kazuo; Iri, Masao
1982
A framework of discrete DC programming by discrete convex analysis. Zbl 1327.90264
Maehara, Takanori; Murota, Kazuo
2015
On the lattice structure of stable allocations in a two-sided discrete-concave market. Zbl 1312.91072
Murota, Kazuo; Yokoi, Yu
2015
Bifurcation theory for hexagonal agglomeration in economic geography. Zbl 1286.91002
Ikeda, Kiyohiro; Murota, Kazuo
2014
Numerical indefinite integration by double exponential sinc method. Zbl 1065.41031
Tanaka, Ken’ichiro; Sugihara, Masaaki; Murota, Kazuo
2005
Optimality criterion for a class of nonlinear integer programs. Zbl 1054.90049
Murota, Kazuo; Saito, Hiroo; Weismantel, Robert
2004
A numerical algorithm for block-diagonal decomposition of matrix $$*$$-algebras with general irreducible components. Zbl 1204.65035
Maehara, Takanori; Murota, Kazuo
2010
Quasi M-convex and L-convex functions – quasiconvexity in discrete optimization. Zbl 1030.90085
Murota, Kazuo; Shioura, Akiyoshi
2003
The linear delta-matroid parity problem. Zbl 1021.05019
Geelen, James F.; Iwata, Satoru; Murota, Kazuo
2003
Fenchel-type duality for matroid valuations. Zbl 0920.90124
Murota, Kazuo
1998
On the degree of mixed polynomial matrices. Zbl 0956.05068
Murota, Kazuo
1998
Mixed matrices: Irreducibility and decomposition. Zbl 0791.15018
Murota, Kazuo
1993
Exact bounds for steepest descent algorithms of $$L$$-convex function minimization. Zbl 1408.90261
Murota, Kazuo; Shioura, Akiyoshi
2014
Discrete convex analysis — exposition on conjugacy and duality. Zbl 0972.90065
Murota, K.
1999
Principal structure of layered mixed matrices. Zbl 0737.15006
Murota, Kazuo
1990
On the irreducibility of layered mixed matrices. Zbl 0702.15008
Murota, Kazuo
1989
Refined study on structural controllability of descriptor systems by means of matroids. Zbl 0635.93007
Murota, Kazuo
1987
Heuristics for planar minimum-weight perfect matchings. Zbl 0503.68050
Iri, Masao; Murota, Kazuo; Matsui, Shouichi
1983
Time bounds for iterative auctions: a unified approach by discrete convex analysis. Zbl 1390.91149
Murota, Kazuo; Shioura, Akiyoshi; Yang, Zaifu
2016
Computing a Walrasian equilibrium in iterative auctions with multiple differentiated items. Zbl 1407.91131
Murota, Kazuo; Shioura, Akiyoshi; Yang, Zaifu
2013
Self-organization of Lösch’s hexagons in economic agglomeration for core-periphery models. Zbl 1258.91169
Ikeda, Kiyohiro; Murota, Kazuo; Akamatsu, Takashi
2012
Algorithm for error-controlled simultaneous block-diagonalization of matrices. Zbl 1227.65039
Maehara, Takanori; Murota, Kazuo
2011
On convergence of the DQDS algorithm for singular value computation. Zbl 1165.65018
Aishima, Kensuke; Matsuo, Takayasu; Murota, Kazuo; Sugihara, Masaaki
2008
Conjugacy relationship between M-convex and L-convex functions in continuous variables. Zbl 1074.90039
Murota, Kazuo; Shioura, Akiyoshi
2004
Proximity theorems of discrete convex functions. Zbl 1084.90038
Murota, Kazuo; Tamura, Akihisa
2004
Characterizing a valuated delta-matroid as a family of delta-matroids. Zbl 0905.90144
Murota, Kazuo
1997
A fast parametric submodular intersection algorithm for strong map sequences. Zbl 0892.90065
Iwata, Satoru; Murota, Kazuo; Shigeno, Maiko
1997
Primal-dual combinatorial relaxation algorithms for the maximum degree of subdeterminants. Zbl 0871.65030
Iwata, Satoru; Murota, Kazuo; Sakuta, Izumi
1996
Echelon modes in uniform materials. Zbl 0943.74542
Ikeda, Kiyohiro; Murota, Kazuo; Nakano, Masaki
1994
On the Smith normal form of structured polynomial matrices. Zbl 0742.15005
Murota, Kazuo
1991
Agglomeration patterns in a long narrow economy of a new economic geography model: analogy to a racetrack economy. Zbl 1398.91402
Ikeda, Kiyohiro; Murota, Kazuo; Akamatsu, Takashi; Takayama, Yuki
2017
Submodular function minimization and maximization in discrete convex analysis. Zbl 1223.90055
Murota, Kazuo
2010
Benders decomposition approach to robust mixed integer programming. Zbl 1172.90452
Saito, Hiroo; Murota, Kazuo
2007
Scaling algorithms for $$M$$-convex function minimization. Zbl 0991.90550
Moriguchi, Satoko; Murota, Kazuo; Shioura, Akiyoshi
2001
Structural approach in systems analysis by mixed matrices – an exposition for index of DAE –. Zbl 0845.34003
Murota, Kazuo
1996
Block-triangularizations of partitioned matrices under similarity/equivalence transformations. Zbl 0811.15008
Ito, Hisashi; Iwata, Satoru; Murota, Kazuo
1994
Structure at infinity of structured descriptor systems and its applications. Zbl 0733.93030
Murota, Kazuo; van der Woude, Jacob W.
1991
Critical imperfection of symmetric structures. Zbl 0778.73025
Murota, Kazuo; Ikeda, Kiyohiro
1991
LU-decomposition of a matrix with entries of different kinds. Zbl 0531.15010
Murota, Kazuo
1983
Linear-time approximation algorithms for finding the minimum-weight perfect matching on a plane. Zbl 0459.68037
Iri, Masao; Murota, Kazuo; Matsui, Shouichi
1981
A shift strategy for superquadratic convergence in the dqds algorithm for singular values. Zbl 1294.65043
Aishima, Kensuke; Matsuo, Takayasu; Murota, Kazuo; Sugihara, Masaaki
2014
Dijkstra’s algorithm and L-concave function maximization. Zbl 1300.90039
Murota, Kazuo; Shioura, Akiyoshi
2014
A Wilkinson-like multishift QR algorithm for symmetric eigenvalue problems and its global convergence. Zbl 1247.65046
Aishima, Kensuke; Matsuo, Takayasu; Murota, Kazuo; Sugihara, Masaaki
2012
Rigorous proof of cubic convergence for the dqds algorithm for singular values. Zbl 1153.65041
Aishima, Kensuke; Matsuo, Takayasu; Murota, Kazuo
2008
Improvement of the scaled corrector method for bifurcation analysis using symmetry-exploiting block-diagonalization. Zbl 1173.74473
Ikeda, Kiyohiro; Murota, Kazuo; Yanagimoto, Akito; Noguchi, Hirohisa
2007
Induction of M-convex functions by linking systems. Zbl 1149.90033
Kobayashi, Yusuke; Murota, Kazuo
2007
Flower patterns appearing on a honeycomb structure and their bifurcation mechanism. Zbl 1082.37512
Saiki, Isao; Ikeda, Kiyohiro; Murota, Kazuo
2005
A capacity scaling algorithm for M-convex submodular flow. Zbl 1079.90112
Iwata, Satoru; Moriguchi, Satoko; Murota, Kazuo
2005
Quadratic M-convex and L-convex functions. Zbl 1126.90399
Murota, Kazuo; Shioura, Akiyoshi
2004
Capacity scaling algorithm for scalable $$M$$-convex submodular flow problems. Zbl 1176.90509
Moriguchi, Satoko; Murota, Kazuo
2003
Scaling, proximity, and optimization of integrally convex functions. Zbl 1421.90129
Moriguchi, Satoko; Murota, Kazuo; Tamura, Akihisa; Tardella, Fabio
2019
Projection and convolution operations for integrally convex functions. Zbl 1411.90227
Moriguchi, Satoko; Murota, Kazuo
2019
On equivalence of $$M^\natural$$-concavity of a set function and submodularity of its conjugate. Zbl 1397.90334
Murota, Kazuo; Shioura, Akiyoshi
2018
Discrete convexity in joint winner property. Zbl 06920229
Iwamasa, Yuni; Murota, Kazuo; Živný, Stanislav
2018
A stronger multiple exchange property for $$\mathrm{M}^{\natural }$$-concave functions. Zbl 1397.90333
Murota, Kazuo
2018
Agglomeration patterns in a long narrow economy of a new economic geography model: analogy to a racetrack economy. Zbl 1398.91402
Ikeda, Kiyohiro; Murota, Kazuo; Akamatsu, Takashi; Takayama, Yuki
2017
Time bounds for iterative auctions: a unified approach by discrete convex analysis. Zbl 1390.91149
Murota, Kazuo; Shioura, Akiyoshi; Yang, Zaifu
2016
An algorithm for the generalized eigenvalue problem for nonsquare matrix pencils by minimal perturbation approach. Zbl 1376.65050
Ito, Shinji; Murota, Kazuo
2016
Scaling and proximity properties of integrally convex functions. Zbl 1398.90121
Moriguchi, Satoko; Murota, Kazuo; Tamura, Akihisa; Tardella, Fabio
2016
A framework of discrete DC programming by discrete convex analysis. Zbl 1327.90264
Maehara, Takanori; Murota, Kazuo
2015
On the lattice structure of stable allocations in a two-sided discrete-concave market. Zbl 1312.91072
Murota, Kazuo; Yokoi, Yu
2015
Continuous relaxation for discrete DC programming. Zbl 1370.90223
Maehara, Takanori; Marumo, Naoki; Murota, Kazuo
2015
Bifurcation theory for hexagonal agglomeration in economic geography. Zbl 1286.91002
Ikeda, Kiyohiro; Murota, Kazuo
2014
Exact bounds for steepest descent algorithms of $$L$$-convex function minimization. Zbl 1408.90261
Murota, Kazuo; Shioura, Akiyoshi
2014
A shift strategy for superquadratic convergence in the dqds algorithm for singular values. Zbl 1294.65043
Aishima, Kensuke; Matsuo, Takayasu; Murota, Kazuo; Sugihara, Masaaki
2014
Dijkstra’s algorithm and L-concave function maximization. Zbl 1300.90039
Murota, Kazuo; Shioura, Akiyoshi
2014
Computing a Walrasian equilibrium in iterative auctions with multiple differentiated items. Zbl 1407.91131
Murota, Kazuo; Shioura, Akiyoshi; Yang, Zaifu
2013
Self-organization of Lösch’s hexagons in economic agglomeration for core-periphery models. Zbl 1258.91169
Ikeda, Kiyohiro; Murota, Kazuo; Akamatsu, Takashi
2012
A Wilkinson-like multishift QR algorithm for symmetric eigenvalue problems and its global convergence. Zbl 1247.65046
Aishima, Kensuke; Matsuo, Takayasu; Murota, Kazuo; Sugihara, Masaaki
2012
On discrete Hessian matrix and convex extensibility. Zbl 1278.90343
Moriguchi, Satoko; Murota, Kazuo
2012
Cone superadditivity of discrete convex functions. Zbl 1267.90073
Kobayashi, Yusuke; Murota, Kazuo; Weismantel, Robert
2012
Algorithm for error-controlled simultaneous block-diagonalization of matrices. Zbl 1227.65039
Maehara, Takanori; Murota, Kazuo
2011
A note on the dqds algorithm with Rutishauser’s shift for singular values. Zbl 1231.65067
Aishima, Kensuke; Matsuo, Takayasu; Murota, Kazuo
2011
Simultaneous singular value decomposition. Zbl 1233.65034
Maehara, Takanori; Murota, Kazuo
2011
A numerical algorithm for block-diagonal decomposition of matrix $$*$$-algebras with application to semidefinite programming. Zbl 1204.65068
Murota, Kazuo; Kanno, Yoshihiro; Kojima, Masakazu; Kojima, Sadayoshi
2010
Matrices and matroids for systems analysis. 2nd printing. Zbl 1181.05001
Murota, Kazuo
2010
Imperfect bifurcation in structures and materials. Engineering use of group-theoretic bifurcation theory. 2nd ed. Zbl 1204.74003
Ikeda, Kiyohiro; Murota, Kazuo
2010
A numerical algorithm for block-diagonal decomposition of matrix $$*$$-algebras with general irreducible components. Zbl 1204.65035
Maehara, Takanori; Murota, Kazuo
2010
Submodular function minimization and maximization in discrete convex analysis. Zbl 1223.90055
Murota, Kazuo
2010
A survey on convergence theorems of the dqds algorithm for computing singular values. Zbl 1210.65088
Aishima, Kensuke; Matsuo, Takayasu; Murota, Kazuo; Sugihara, Masaaki
2010
Error-controlling algorithm for simultaneous block-diagonalization and its application to independent component analysis. Zbl 1271.65080
Maehara, Takanori; Murota, Kazuo
2010
Superquadratic convergence of DLASQ for computing matrix singular values. Zbl 1198.65078
Aishima, Kensuke; Matsuo, Takayasu; Murota, Kazuo; Sugihara, Masaaki
2010
Recent developments in discrete convex analysis. Zbl 1359.05020
Murota, Kazuo
2009
Function classes for successful DE-sinc approximations. Zbl 1198.65037
Tanaka, Ken’ichiro; Sugihara, Masaaki; Murota, Kazuo
2009
Function classes for double exponential integration formulas. Zbl 1162.65014
Tanaka, Ken’ichiro; Sugihara, Masaaki; Murota, Kazuo; Mori, Masatake
2009
Complex analytic approach to the sinc-Gauss sampling formula. Zbl 1152.65123
Tanaka, Ken’ichiro; Sugihara, Masaaki; Murota, Kazuo
2008
On convergence of the DQDS algorithm for singular value computation. Zbl 1165.65018
Aishima, Kensuke; Matsuo, Takayasu; Murota, Kazuo; Sugihara, Masaaki
2008
Rigorous proof of cubic convergence for the dqds algorithm for singular values. Zbl 1153.65041
Aishima, Kensuke; Matsuo, Takayasu; Murota, Kazuo
2008
Note on the continuity of M-convex and L-convex functions in continuous variables. Zbl 1161.90472
Murota, Kazuo; Shioura, Akiyoshi
2008
Operations on M-convex functions on jump systems. Zbl 1144.90015
Kobayashi, Yusuke; Murota, Kazuo; Tanaka, Ken’ichiro
2007
Benders decomposition approach to robust mixed integer programming. Zbl 1172.90452
Saito, Hiroo; Murota, Kazuo
2007
Improvement of the scaled corrector method for bifurcation analysis using symmetry-exploiting block-diagonalization. Zbl 1173.74473
Ikeda, Kiyohiro; Murota, Kazuo; Yanagimoto, Akito; Noguchi, Hirohisa
2007
Induction of M-convex functions by linking systems. Zbl 1149.90033
Kobayashi, Yusuke; Murota, Kazuo
2007
$$M$$-convex functions on jump systems: a general framework for minsquare graph factor problem. Zbl 1119.90031
Murota, Kazuo
2006
Discrete fixed point theorem reconsidered. Zbl 1119.58006
Iimura, Takuya; Murota, Kazuo; Tamura, Akihisa
2005
Note on multimodularity and L-convexity. Zbl 1082.90071
Murota, Kazuo
2005
Deterministic network coding by matrix completion. Zbl 1297.68022
Harvey, Nicholas J. A.; Karger, David R.; Murota, Kazuo
2005
Numerical indefinite integration by double exponential sinc method. Zbl 1065.41031
Tanaka, Ken’ichiro; Sugihara, Masaaki; Murota, Kazuo
2005
Flower patterns appearing on a honeycomb structure and their bifurcation mechanism. Zbl 1082.37512
Saiki, Isao; Ikeda, Kiyohiro; Murota, Kazuo
2005
A capacity scaling algorithm for M-convex submodular flow. Zbl 1079.90112
Iwata, Satoru; Moriguchi, Satoko; Murota, Kazuo
2005
SVM kernel by electric network. Zbl 1274.90528
Hirai, Hiroshi; Murota, Kazuo; Rikitoku, Masaki
2005
Substitutes and complements in network flows viewed as discrete convexity. Zbl 1131.90052
Murota, Kazuo; Shioura, Akiyoshi
2005
Use of primal-dual technique in the network algorithm for two-way contingency tables. Zbl 1059.62060
Suzuki, Taiji; Aoki, Satoshi; Murota, Kazuo
2005
$$M$$-convex functions and tree metrics. Zbl 1084.90036
Hirai, Hiroshi; Murota, Kazuo
2004
Optimality criterion for a class of nonlinear integer programs. Zbl 1054.90049
Murota, Kazuo; Saito, Hiroo; Weismantel, Robert
2004
Conjugacy relationship between M-convex and L-convex functions in continuous variables. Zbl 1074.90039
Murota, Kazuo; Shioura, Akiyoshi
2004
Proximity theorems of discrete convex functions. Zbl 1084.90038
Murota, Kazuo; Tamura, Akihisa
2004
Quadratic M-convex and L-convex functions. Zbl 1126.90399
Murota, Kazuo; Shioura, Akiyoshi
2004
A capacity scaling algorithm for M-convex submodular flow. Zbl 1092.90007
Iwata, Satoru; Moriguchi, Satoko; Murota, Kazuo
2004
Discrete convex analysis. Zbl 1029.90055
Murota, Kazuo
2003
Exploiting sparsity in semidefinite programming via matrix completion. II: Implementation and numerical results. Zbl 1030.90081
Nakata, Kazuhide; Fujisawa, Katsuki; Fukuda, Mituhiro; Kojima, Masakazu; Murota, Kazuo
2003
New characterizations of M-convex functions and their applications to economic equilibrium models with indivisibilities. Zbl 1094.90023
Murota, Kazuo; Tamura, Akihisa
2003
On steepest descent algorithms for discrete convex functions. Zbl 1071.90027
Murota, Kazuo
2003
Application of M-convex submodular flow problem to mathematical economics. Zbl 1092.91058
Murota, Kazuo; Tamura, Akihisa
2003
Quasi M-convex and L-convex functions – quasiconvexity in discrete optimization. Zbl 1030.90085
Murota, Kazuo; Shioura, Akiyoshi
2003
The linear delta-matroid parity problem. Zbl 1021.05019
Geelen, James F.; Iwata, Satoru; Murota, Kazuo
2003
Capacity scaling algorithm for scalable $$M$$-convex submodular flow problems. Zbl 1176.90509
Moriguchi, Satoko; Murota, Kazuo
2003
Imperfect bifurcation in structures and materials. Engineering use of group-theoretic bifucation theory. Zbl 1005.74001
Ikeda, Kiyohiro; Murota, Kazuo
2002
Discrete convexity and equilibria in economies with indivisible goods and money. Zbl 1004.91052
Danilov, Vladimir; Koshevoy, Gleb; Murota, Kazuo
2001
Group symmetry in interior-point methods for semidefinite program. Zbl 1035.90056
Kanno, Yoshihiro; Ohsaki, Makoto; Murota, Kazuo; Katoh, Naoki
2001
Relationship of M-/L-convex functions with discrete convex functions by Miller and Favati-Tardella. Zbl 1076.90036
Murota, Kazuo; Shioura, Akiyoshi
2001
On circuit valuation of matroids. Zbl 0979.05028
Murota, Kazuo; Tamura, Akihisa
2001
Scaling algorithms for $$M$$-convex function minimization. Zbl 0991.90550
Moriguchi, Satoko; Murota, Kazuo; Shioura, Akiyoshi
2001
Combinatorial relaxation algorithm for mixed polynomial matrices. Zbl 1160.90637
Iwata, Satoru; Murota, Kazuo
2001
Application of M-convex submodular flow problem to mathematical economics. Zbl 1076.91526
Murota, Kazuo; Tamura, Akihisa
2001
Formalization of economic equilibria with indivisible commodities by using $$M$$-convex modular flows. Zbl 0991.91507
Murota, Kazuo; Tamura, Akihisa
2001
Matrices and matroids for systems analysis. Zbl 0948.05001
Murota, Kazuo
2000
Exploiting sparsity in semidefinite programming via matrix completion. I: General framework. Zbl 1010.90053
Fukuda, Mituhiro; Kojima, Masakazu; Murota, Kazuo; Nakata, Kazuhide
2000
Notes on L-/M-convex functions and the separation theorems. Zbl 0974.90019
Fujishige, Satoru; Murota, Kazuo
2000
Extension of M-convexity and L-convexity to polyhedral convex functions. Zbl 1073.90544
Murota, Kazuo; Shioura, Akiyoshi
2000
Symmetric failures in symmetric control systems. Zbl 0962.93011
Tanaka, R.; Murota, K.
2000
Quantitative analysis for controllability of symmetric control systems. Zbl 1006.93506
Tanaka, Reiko; Murota, Kazuo
2000
$$M$$-convex function on generalized polymatroid. Zbl 0977.90044
Murota, Kazuo; Shioura, Akiyoshi
1999
Submodular flow problem with a nonseparable cost function. Zbl 0947.90119
Murota, Kazuo
1999
Discrete convex analysis — exposition on conjugacy and duality. Zbl 0972.90065
Murota, K.
1999
Bifurcation mechanism underlying echelon-mode formation. Zbl 0949.74024
Murota, Kazuo; Ikeda, Kiyohiro; Terada, Kenjiro
1999
Discrete convex analysis. Zbl 0920.90103
Murota, Kazuo
1998
Fenchel-type duality for matroid valuations. Zbl 0920.90124
Murota, Kazuo
1998
On the degree of mixed polynomial matrices. Zbl 0956.05068
Murota, Kazuo
1998
Matroid valuation on independent sets. Zbl 0867.05017
Murota, Kazuo
1997
Characterizing a valuated delta-matroid as a family of delta-matroids. Zbl 0905.90144
Murota, Kazuo
1997
A fast parametric submodular intersection algorithm for strong map sequences. Zbl 0892.90065
Iwata, Satoru; Murota, Kazuo; Shigeno, Maiko
1997
$$M$$-convex function on generalized polymatroid. Zbl 0971.90073
Murota, Kazuo; Shioura, Akiyoshi
1997
Convexity and Steinitz’s exchange property. Zbl 0867.90092
Murota, Kazuo
1996
Valuated matroid intersection. I: Optimality criteria. Zbl 0868.90132
Murota, Kazuo
1996
Valuated matroid intersection. II: Algorithms. Zbl 0868.90133
Murota, Kazuo
1996
Primal-dual combinatorial relaxation algorithms for the maximum degree of subdeterminants. Zbl 0871.65030
Iwata, Satoru; Murota, Kazuo; Sakuta, Izumi
1996
Structural approach in systems analysis by mixed matrices – an exposition for index of DAE –. Zbl 0845.34003
Murota, Kazuo
1996
Note on exchange axioms for valuated matroids and valuated delta-matroids. Zbl 0880.05024
Murota, K.
1996
Horizontal principal structure of layered mixed matrices: Decomposition of discrete systems by design-variable selections. Zbl 0849.15007
Iwata, Satoru; Murota, Kazuo
1996
...and 55 more Documents
all top 5

#### Cited by 1,023 Authors

 74 Murota, Kazuo 22 Shioura, Akiyoshi 19 Drezner, Zvi 19 Iwata, Satoru 18 Ikeda, Kiyohiro 14 Sugihara, Masaaki 14 Tamura, Akihisa 13 Boukhobza, Taha 13 Hirai, Hiroshi 13 Okayama, Tomoaki 12 Commault, Christian 11 Fujishige, Satoru 11 Kojima, Masakazu 10 Matsuo, Takayasu 10 Takazawa, Kenjiro 9 Hamelin, Frederic 9 Kim, Sunyoung 9 Van der Woude, Jacob Willem 8 Dion, Jean-Michel 8 Kobayashi, Yusuke 8 Koshevoy, Gleb A. 8 Yamashita, Makoto 7 Drezner, Tammy 7 Kamiyama, Naoyuki 7 Sugihara, Kokichi 6 Danilov, Vladimir I. 6 Rincón, Felipe 6 Takamatsu, Mizuyo 6 Tanaka, Ken’ichiro 6 Weismantel, Robert 6 Yang, Zaifu 6 Yokoi, Yu 5 de Klerk, Etienne 5 Iri, Masao 5 Maehara, Takanori 5 Moriguchi, Satoko 5 Ogata, Hidenori 5 Peis, Britta 5 Reinschke, Kurt J. 5 Sakakibara, Koya 5 Takayama, Yuki 4 Aishima, Kensuke 4 Asharabi, Rashad M. 4 Cai, Jin-Yi 4 Dahl, Joachim 4 Harks, Tobias 4 Hemmecke, Raymond 4 Iimura, Takuya 4 Kakimura, Naonori 4 Kanno, Yoshihiro 4 Kashiwabara, Kenji 4 Lu, Pinyan 4 Nakata, Kazuhide 4 Ohsaki, Miho 4 Talman, Dolf 4 Van der Laan, Gerard 3 Amano, Kaname 3 Andersen, Martin S. 3 Anjos, Miguel F. 3 Brändén, Petter 3 Brimberg, Jack 3 Chen, Xin 3 Cravo, Glória 3 Dress, Andreas W. M. 3 Du, Ding-Zhu 3 Eriksson, Anders B. 3 Eshima, Nobuoki 3 Fantuzzi, Giovanni 3 Farooq, Rashid 3 Farràs, Oriol 3 Fujii, Fumio 3 Ghosh, Sucharita 3 Imai, Hideki 3 Kobayashi, Kazuhiro 3 Laporte, Gilbert 3 Martinez-Martinez, Sinuhé 3 Mori, Masatake 3 Murat, Alper Ekrem 3 Nishida, Tetsushi 3 Nordmark, Arne B. 3 Ohsaki, Makoto 3 Okamoto, Yoshio 3 Okano, Dai 3 Onda, Mikihisa 3 Onn, Shmuel 3 Oum, Sang-Il 3 Padró, Carles 3 Paes Leme, Renato 3 Parrilo, Pablo A. 3 Pasechnik, Dmitrii V. 3 Röbenack, Klaus 3 Saiki, Isao 3 Sauter, Dominique D. J. 3 Scott, Carlton H. 3 Soma, Tasuku 3 Tabata, Minoru 3 Tardella, Fabio 3 Terada, Kenjiro 3 Ui, Takashi 3 Verter, Vedat ...and 923 more Authors
all top 5

#### Cited in 211 Serials

 49 Mathematical Programming. Series A. Series B 39 Discrete Applied Mathematics 34 Japan Journal of Industrial and Applied Mathematics 28 Linear Algebra and its Applications 20 Journal of Computational and Applied Mathematics 19 European Journal of Operational Research 18 Automatica 14 Computer Methods in Applied Mechanics and Engineering 14 Discrete Optimization 13 Mathematics of Operations Research 12 Theoretical Computer Science 12 Algorithmica 10 Operations Research Letters 9 Journal of Global Optimization 8 Advances in Mathematics 8 Journal of Combinatorial Theory. Series A 8 SIAM Journal on Discrete Mathematics 8 SIAM Journal on Optimization 8 Optimization Methods & Software 7 International Journal for Numerical Methods in Engineering 7 Journal of Combinatorial Theory. Series B 7 Journal of Mathematical Economics 7 Discrete & Computational Geometry 7 Computers & Operations Research 7 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 6 Operations Research 6 Advances in Applied Mathematics 6 Applied Mathematics Letters 5 Journal of the Mechanics and Physics of Solids 5 Applied Mathematics and Computation 5 BIT 5 Journal of Computer and System Sciences 5 Numerische Mathematik 5 Systems & Control Letters 5 Computational Geometry 5 Computational Optimization and Applications 5 Journal of the Operations Research Society of China 5 JSIAM Letters 4 Discrete Mathematics 4 International Journal of Systems Science 4 Information Processing Letters 4 Journal of Computational Physics 4 Mathematics of Computation 4 Journal of Economic Theory 4 Journal of Optimization Theory and Applications 4 SIAM Journal on Matrix Analysis and Applications 4 Annals of Operations Research 4 Communications in Statistics. Theory and Methods 4 Theory of Computing Systems 4 Mathematical Methods of Operations Research 4 Journal of Combinatorial Optimization 3 Artificial Intelligence 3 International Journal of Control 3 Combinatorica 3 Journal of Complexity 3 Computational Mechanics 3 International Journal of Computational Geometry & Applications 3 Numerical Algorithms 3 Games and Economic Behavior 3 Communications in Statistics. Simulation and Computation 3 European Journal of Control 3 Structural and Multidisciplinary Optimization 3 Networks and Spatial Economics 3 Mathematical Programming Computation 2 Acta Mechanica 2 The Canadian Journal of Statistics 2 Computers & Mathematics with Applications 2 Journal of the Franklin Institute 2 Journal of Mathematical Physics 2 Linear and Multilinear Algebra 2 Mathematical Notes 2 Annals of the Institute of Statistical Mathematics 2 Computing 2 Fuzzy Sets and Systems 2 International Journal of Circuit Theory and Applications 2 Journal of Approximation Theory 2 Journal of Differential Equations 2 Journal of Multivariate Analysis 2 Journal of Pure and Applied Algebra 2 Naval Research Logistics 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 SIAM Journal on Computing 2 European Journal of Combinatorics 2 Mathematical Social Sciences 2 Asia-Pacific Journal of Operational Research 2 Journal of Economic Dynamics & Control 2 Discrete Event Dynamic Systems 2 Aequationes Mathematicae 2 International Journal of Computer Mathematics 2 Pattern Recognition 2 Computational Statistics and Data Analysis 2 Computational Complexity 2 Journal of Algebraic Combinatorics 2 Computational and Applied Mathematics 2 Advances in Computational Mathematics 2 INFORMS Journal on Computing 2 Annals of Combinatorics 2 Discrete Dynamics in Nature and Society 2 Optimization and Engineering 2 International Game Theory Review ...and 111 more Serials
all top 5

#### Cited in 51 Fields

 280 Operations research, mathematical programming (90-XX) 139 Combinatorics (05-XX) 132 Numerical analysis (65-XX) 106 Computer science (68-XX) 87 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 77 Convex and discrete geometry (52-XX) 66 Systems theory; control (93-XX) 54 Linear and multilinear algebra; matrix theory (15-XX) 49 Mechanics of deformable solids (74-XX) 31 Statistics (62-XX) 21 Approximations and expansions (41-XX) 20 Information and communication theory, circuits (94-XX) 19 Algebraic geometry (14-XX) 17 Partial differential equations (35-XX) 12 Group theory and generalizations (20-XX) 12 Integral equations (45-XX) 12 Probability theory and stochastic processes (60-XX) 11 Real functions (26-XX) 11 Ordinary differential equations (34-XX) 11 Calculus of variations and optimal control; optimization (49-XX) 9 Functions of a complex variable (30-XX) 7 Dynamical systems and ergodic theory (37-XX) 7 Operator theory (47-XX) 6 Field theory and polynomials (12-XX) 6 Geometry (51-XX) 5 Order, lattices, ordered algebraic structures (06-XX) 5 Commutative algebra (13-XX) 5 Fluid mechanics (76-XX) 4 Number theory (11-XX) 4 Difference and functional equations (39-XX) 4 Functional analysis (46-XX) 4 General topology (54-XX) 4 Quantum theory (81-XX) 4 Biology and other natural sciences (92-XX) 3 Mathematical logic and foundations (03-XX) 3 Associative rings and algebras (16-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Mechanics of particles and systems (70-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Algebraic topology (55-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 History and biography (01-XX) 1 General algebraic systems (08-XX) 1 Nonassociative rings and algebras (17-XX) 1 Measure and integration (28-XX) 1 Special functions (33-XX) 1 Sequences, series, summability (40-XX) 1 Manifolds and cell complexes (57-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Mathematics education (97-XX)

#### Wikidata Timeline

The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.