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Uhlig, Frank

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Author ID: uhlig.frank Recent zbMATH articles by "Uhlig, Frank"
Published as: Uhlig, F.; Uhlig, Frank
Homepage: http://www.auburn.edu/~uhligfd/
External Links: MGP · ORCID · ResearchGate · dblp · GND
Documents Indexed: 64 Publications since 1973, including 8 Books
Reviewing Activity: 277 Reviews

Publications by Year

Citations contained in zbMATH Open

47 Publications have been cited 415 times in 325 Documents Cited by Year
A recurring theorem about pairs of quadratic forms and extensions: A survey. Zbl 0408.15022
Uhlig, Frank
61
1979
Improved methods and starting values to solve the matrix equations \(X\pm A^*X^{-1}A=I\) iteratively. Zbl 1058.65051
Ivanov, Ivan G.; Hasanov, Vejdi I.; Uhlig, Frank
42
2005
A canonical form for a pair of real symmetric matrices that generate a nonsingular pencil. Zbl 0338.15009
Uhlig, Frank
26
1976
Numerical ranges of an operator on an indefinite inner product space. Zbl 0851.15018
Li, Chi-Kwong; Tsing, Nam-Kui; Uhlig, Frank
19
1996
On the matrix equation \(AX=B\) with applications to the generators of a controllability matrix. Zbl 0612.15006
Uhlig, Frank
19
1987
Simultaneous block diagonalization of two real symmetric matrices. Zbl 0291.15010
Uhlig, Frank
18
1973
Numerical algorithms with C. Transl. from the German by Maria Schon a. Frank Uhlig. Incl. 1 CD-ROM. Zbl 0857.65003
Engeln-Müllges, Gisela; Uhlig, Frank
15
1996
Improved perturbation estimates for the matrix equations \(X \pm A^{*} X^{-1} A=Q\). Zbl 1039.15005
Hasanov, V. I.; Ivanov, I. G.; Uhlig, F.
14
2004
Constructive ways for generating (generalized) real orthogonal matrices as products of (generalized) symmetries. Zbl 0982.65049
Uhlig, Frank
12
2001
Numerical algorithms with Fortran. Transl. from the German by Maria Schon a. Frank Uhlig. Incl. 1 CD-ROM. Zbl 0857.65002
Engeln-Müllges, Gisela; Uhlig, Frank
12
1996
Inverse eigenvalue problems associated with spring-mass systems. Zbl 0879.15007
Nylen, Peter; Uhlig, Frank
11
1997
Definite and semidefinite matrices in a real symmetric matrix pencil. Zbl 0291.15013
Uhlig, Frank
11
1973
An inverse field of values problem. Zbl 1159.65045
Uhlig, Frank
10
2008
Inverse eigenvalue problem: Existence of special spring-mass systems. Zbl 0880.35136
Nylen, Peter; Uhlig, Frank
10
1997
On the matrix equation \(f(x)=A\). Zbl 0753.15009
Evard, Jean-Claude; Uhlig, Frank
9
1992
A method for the inverse numerical range problem. Zbl 1207.65042
Chorianopoulos, Christos; Psarrakos, Panayiotis; Uhlig, Frank
8
2010
A rational canonical pair form for a pair of symmetric matrices over an arbitrary field F with char \(F\neq 2\) and applications to finest simultaneous block diagonalizations. Zbl 0418.15008
Uhlig, Frank
8
1979
On the maximal number of linearly independent real vectors annihilated simultaneously by two real quadratic forms. Zbl 0291.15012
Uhlig, Frank
8
1973
The number of vectors jointly annihilated by two real quadratic forms determines the inertia of matrices in the associated pencil. Zbl 0291.15011
Uhlig, Frank
8
1973
Inertia and eigenvalue relations between symmetrized and symmetrizing matrices for the real and the general field case. Zbl 0501.15016
Uhlig, Frank
7
1981
The DQR algorithm, basic theory, convergence, and conditional stability. Zbl 0883.65029
Uhlig, Frank
6
1997
A best upper bound for the 2-norm condition number of a matrix. Zbl 0877.15006
Merikoski, Jorma Kaarlo; Urpala, Uoti; Virtanen, Ari; Tam, Tin-Yau; Uhlig, Frank
6
1997
The field of values of a complex matrix, an explicit description in the 2\(\times 2\) case. Zbl 0581.15009
Uhlig, Frank
6
1985
The QR algorithm: 50 years later its genesis by John Francis and Vera Kublanovskaya and subsequent developments. Zbl 1169.65032
Golub, Gene; Uhlig, Frank
5
2009
General polynomial roots and their multiplicities in \(O(N)\) memory and \(O(N^2)\) time. Zbl 1055.12504
Uhlig, Frank
5
1999
Sign patterns, nonsingularity, and the solvability of Ax=b. Zbl 0488.15002
Johnson, Charles R.; Uhlig, Frank; Warner, Dan
5
1982
On the nonsingular symmetric factors of a real matrix. Zbl 0284.15015
Uhlig, Frank
5
1974
A 5-instant finite difference formula to find discrete time-varying generalized matrix inverses, matrix inverses, and scalar reciprocals. Zbl 1434.65022
Li, Jian; Mao, Mingzhi; Uhlig, Frank; Zhang, Yunong
4
2019
Z-type neural-dynamics for time-varying nonlinear optimization under a linear equality constraint with robot application. Zbl 1378.90077
Li, Jian; Mao, Mingzhi; Uhlig, Frank; Zhang, Yunong
4
2018
Geometric computation of the numerical radius of a matrix. Zbl 1178.65041
Uhlig, Frank
4
2009
Realizations of interlacing by tree-patterned matrices. Zbl 0817.05044
Nylen, Peter; Uhlig, Frank
4
1994
On the eigenvalues of principal submatrices of normal, Hermitian and symmetric matrices. Zbl 0794.15003
Nylen, Peter; Tam, Tin-Yau; Uhlig, Frank
4
1993
Explicit polar decomposition and a near-characteristic polynomial: the \(2\times 2\) case. Zbl 0512.15005
Uhlig, Frank
4
1981
Time-varying matrix eigenanalyses via Zhang neural networks and look-ahead finite difference equations. Zbl 1420.65070
Uhlig, Frank; Zhang, Yunong
3
2019
Faster and more accurate computation of the field of values boundary for n by n matrices. Zbl 1295.65051
Uhlig, Frank
3
2014
On computing the generalized Crawford number of a matrix. Zbl 1261.65044
Uhlig, Frank
3
2013
Inertia, numerical range, and zeros of quadratic forms for matrix pencils. Zbl 0725.15014
Tsing, Nam-Kiu; Uhlig, Frank
3
1991
The construction of high order convergent look-ahead finite difference formulas for Zhang neural networks. Zbl 1425.65207
Uhlig, Frank
2
2019
Computing the inertias in symmetric matrix pencils. Zbl 0821.15009
Uhlig, Frank
2
1994
Are the coefficients of a polynomial well-conditioned functions of its roots? Zbl 0766.65043
Uhlig, Frank
2
1992
Zhang neural networks for fast and accurate computations of the field of values. Zbl 1450.65036
Uhlig, Frank
1
2020
Computing matrix symmetrizers, finally possible via the Huang and Nong algorithm. Zbl 1386.65126
Uhlig, Frank
1
2013
Completion of an orthogonal projector and a related inverse mapping problem. Zbl 1098.15011
Meng, Chunjun; Hu, Xiyan; Zhang, Lei; Uhlig, Frank
1
2005
Transform linear algebra. Zbl 1083.15002
Uhlig, Frank
1
2002
Partial convergence and sign convergence of matrix powers via eigen c-ads. Zbl 0896.65036
Uhlig, Frank
1
1998
Emilie Haynsworth, 1916-1985 (Obituary). Zbl 0582.01019
Carlson, David; Markham, Thomas L.; Uhlig, Frank
1
1986
Relations between the fields of values of a matrix and of its polar factors: The 2x2 real and complex case. Zbl 0528.15006
Uhlig, Frank
1
1983
Zhang neural networks for fast and accurate computations of the field of values. Zbl 1450.65036
Uhlig, Frank
1
2020
A 5-instant finite difference formula to find discrete time-varying generalized matrix inverses, matrix inverses, and scalar reciprocals. Zbl 1434.65022
Li, Jian; Mao, Mingzhi; Uhlig, Frank; Zhang, Yunong
4
2019
Time-varying matrix eigenanalyses via Zhang neural networks and look-ahead finite difference equations. Zbl 1420.65070
Uhlig, Frank; Zhang, Yunong
3
2019
The construction of high order convergent look-ahead finite difference formulas for Zhang neural networks. Zbl 1425.65207
Uhlig, Frank
2
2019
Z-type neural-dynamics for time-varying nonlinear optimization under a linear equality constraint with robot application. Zbl 1378.90077
Li, Jian; Mao, Mingzhi; Uhlig, Frank; Zhang, Yunong
4
2018
Faster and more accurate computation of the field of values boundary for n by n matrices. Zbl 1295.65051
Uhlig, Frank
3
2014
On computing the generalized Crawford number of a matrix. Zbl 1261.65044
Uhlig, Frank
3
2013
Computing matrix symmetrizers, finally possible via the Huang and Nong algorithm. Zbl 1386.65126
Uhlig, Frank
1
2013
A method for the inverse numerical range problem. Zbl 1207.65042
Chorianopoulos, Christos; Psarrakos, Panayiotis; Uhlig, Frank
8
2010
The QR algorithm: 50 years later its genesis by John Francis and Vera Kublanovskaya and subsequent developments. Zbl 1169.65032
Golub, Gene; Uhlig, Frank
5
2009
Geometric computation of the numerical radius of a matrix. Zbl 1178.65041
Uhlig, Frank
4
2009
An inverse field of values problem. Zbl 1159.65045
Uhlig, Frank
10
2008
Improved methods and starting values to solve the matrix equations \(X\pm A^*X^{-1}A=I\) iteratively. Zbl 1058.65051
Ivanov, Ivan G.; Hasanov, Vejdi I.; Uhlig, Frank
42
2005
Completion of an orthogonal projector and a related inverse mapping problem. Zbl 1098.15011
Meng, Chunjun; Hu, Xiyan; Zhang, Lei; Uhlig, Frank
1
2005
Improved perturbation estimates for the matrix equations \(X \pm A^{*} X^{-1} A=Q\). Zbl 1039.15005
Hasanov, V. I.; Ivanov, I. G.; Uhlig, F.
14
2004
Transform linear algebra. Zbl 1083.15002
Uhlig, Frank
1
2002
Constructive ways for generating (generalized) real orthogonal matrices as products of (generalized) symmetries. Zbl 0982.65049
Uhlig, Frank
12
2001
General polynomial roots and their multiplicities in \(O(N)\) memory and \(O(N^2)\) time. Zbl 1055.12504
Uhlig, Frank
5
1999
Partial convergence and sign convergence of matrix powers via eigen c-ads. Zbl 0896.65036
Uhlig, Frank
1
1998
Inverse eigenvalue problems associated with spring-mass systems. Zbl 0879.15007
Nylen, Peter; Uhlig, Frank
11
1997
Inverse eigenvalue problem: Existence of special spring-mass systems. Zbl 0880.35136
Nylen, Peter; Uhlig, Frank
10
1997
The DQR algorithm, basic theory, convergence, and conditional stability. Zbl 0883.65029
Uhlig, Frank
6
1997
A best upper bound for the 2-norm condition number of a matrix. Zbl 0877.15006
Merikoski, Jorma Kaarlo; Urpala, Uoti; Virtanen, Ari; Tam, Tin-Yau; Uhlig, Frank
6
1997
Numerical ranges of an operator on an indefinite inner product space. Zbl 0851.15018
Li, Chi-Kwong; Tsing, Nam-Kui; Uhlig, Frank
19
1996
Numerical algorithms with C. Transl. from the German by Maria Schon a. Frank Uhlig. Incl. 1 CD-ROM. Zbl 0857.65003
Engeln-Müllges, Gisela; Uhlig, Frank
15
1996
Numerical algorithms with Fortran. Transl. from the German by Maria Schon a. Frank Uhlig. Incl. 1 CD-ROM. Zbl 0857.65002
Engeln-Müllges, Gisela; Uhlig, Frank
12
1996
Realizations of interlacing by tree-patterned matrices. Zbl 0817.05044
Nylen, Peter; Uhlig, Frank
4
1994
Computing the inertias in symmetric matrix pencils. Zbl 0821.15009
Uhlig, Frank
2
1994
On the eigenvalues of principal submatrices of normal, Hermitian and symmetric matrices. Zbl 0794.15003
Nylen, Peter; Tam, Tin-Yau; Uhlig, Frank
4
1993
On the matrix equation \(f(x)=A\). Zbl 0753.15009
Evard, Jean-Claude; Uhlig, Frank
9
1992
Are the coefficients of a polynomial well-conditioned functions of its roots? Zbl 0766.65043
Uhlig, Frank
2
1992
Inertia, numerical range, and zeros of quadratic forms for matrix pencils. Zbl 0725.15014
Tsing, Nam-Kiu; Uhlig, Frank
3
1991
On the matrix equation \(AX=B\) with applications to the generators of a controllability matrix. Zbl 0612.15006
Uhlig, Frank
19
1987
Emilie Haynsworth, 1916-1985 (Obituary). Zbl 0582.01019
Carlson, David; Markham, Thomas L.; Uhlig, Frank
1
1986
The field of values of a complex matrix, an explicit description in the 2\(\times 2\) case. Zbl 0581.15009
Uhlig, Frank
6
1985
Relations between the fields of values of a matrix and of its polar factors: The 2x2 real and complex case. Zbl 0528.15006
Uhlig, Frank
1
1983
Sign patterns, nonsingularity, and the solvability of Ax=b. Zbl 0488.15002
Johnson, Charles R.; Uhlig, Frank; Warner, Dan
5
1982
Inertia and eigenvalue relations between symmetrized and symmetrizing matrices for the real and the general field case. Zbl 0501.15016
Uhlig, Frank
7
1981
Explicit polar decomposition and a near-characteristic polynomial: the \(2\times 2\) case. Zbl 0512.15005
Uhlig, Frank
4
1981
A recurring theorem about pairs of quadratic forms and extensions: A survey. Zbl 0408.15022
Uhlig, Frank
61
1979
A rational canonical pair form for a pair of symmetric matrices over an arbitrary field F with char \(F\neq 2\) and applications to finest simultaneous block diagonalizations. Zbl 0418.15008
Uhlig, Frank
8
1979
A canonical form for a pair of real symmetric matrices that generate a nonsingular pencil. Zbl 0338.15009
Uhlig, Frank
26
1976
On the nonsingular symmetric factors of a real matrix. Zbl 0284.15015
Uhlig, Frank
5
1974
Simultaneous block diagonalization of two real symmetric matrices. Zbl 0291.15010
Uhlig, Frank
18
1973
Definite and semidefinite matrices in a real symmetric matrix pencil. Zbl 0291.15013
Uhlig, Frank
11
1973
On the maximal number of linearly independent real vectors annihilated simultaneously by two real quadratic forms. Zbl 0291.15012
Uhlig, Frank
8
1973
The number of vectors jointly annihilated by two real quadratic forms determines the inertia of matrices in the associated pencil. Zbl 0291.15011
Uhlig, Frank
8
1973
all top 5

Cited by 450 Authors

25 Uhlig, Frank
13 Bebiano, Natália Isabel Quadros
13 Wang, Qingwen
12 da Providência Santarém e Costa, João
9 Duan, Xuefeng
8 Liao, Anping
8 Vũ Ngoc Phát
7 Nakazato, Hiroshi
6 Hasanov, Vejdi Ismailov
6 Rodman, Leiba X.
6 Simos, Theodore E.
6 Zhang, Yunong
5 Anastassi, Zacharias A.
5 Ivanov, Ivan Ganchev
5 Sen, Mausumi
5 Sharma, Debashish
4 Li, Jing
4 Liu, Sanyang
4 Merino, Dennis I.
4 Nata, Ana
4 Niamsup, Piyapong
4 Paras, Agnes T.
4 Petersen, Ian Richard
4 Rajchakit, Grienggrai
4 Rajchakit, Manlika
4 Savkin, Andrey V.
4 Spitkovsky, Ilya Matvey
4 Yin, Xiaoyan
3 Aragón González, Gerardo
3 Chen, Guoliang
3 Chien, Mao-Ting
3 da Providencia e Costa, Joao Pinheiro
3 Gemignani, Luca
3 Jiang, Rujun
3 Johnson, Charles Royal
3 Katsouleas, Georgios
3 Laffey, Thomas J.
3 Lazard, Sylvain
3 Li, Duan
3 Maroulas, John
3 Pan, Victor Yakovlevich
3 Petitjean, Sylvain
3 Rodríguez-Andrade, M. A.
3 Song, Guangjing
2 Al-Saggaf, Ubaid Muhsen
2 Aragón, Juan L.
2 Berzig, Maher
2 Boito, Paola
2 Cai, Jing
2 Carden, Russell L.
2 Chu, Moody T.
2 Dehghan Takht Fooladi, Mehdi
2 Dela Rosa, Kennett L.
2 Dupont, Laurent
2 Eidelman, Yuli
2 Evard, Jean-Claude
2 Fang, Liang
2 Fasi, Massimiliano
2 Fuhrmann, Paul A.
2 Guo, Chun-Hua
2 Higham, Nicholas J.
2 Hu, Xiyan
2 Huang, Aimin
2 Huang, Huanchang
2 Iannazzo, Bruno
2 Kim, Hyun-Min
2 Kosti, Athinoula A.
2 Lady, George M.
2 Lam, James
2 Lazard, Daniel
2 Le Van Hien
2 Lemos, Rute
2 Li, Chi-Kwong
2 Li, Chunmei
2 Li, Jian
2 Lin, Chunyan
2 Ling, Yihong
2 Lins, Brian
2 Liu, Jianzhou
2 Liu, Xin
2 Lu, Ding
2 Mao, Mingzhi
2 Marcus, Marvin D.
2 Maxwell, Peter
2 Mehl, Christian
2 Mourrain, Bernard
2 Nylen, Peter M.
2 Pivovarchik, Vyacheslav M.
2 Pötzsche, Christian
2 Ran, André C. M.
2 Ratchagit, Kreangkri
2 Reams, Robert B.
2 Samet, Bessem
2 Sun, Jiguang
2 Tao, Jiyuan
2 Thành, Nguyen Trung
2 Thompson, Robert C.
2 Tian, Yongge
2 Tu, Changhe
2 Wang, Wenping
...and 350 more Authors
all top 5

Cited in 106 Serials

101 Linear Algebra and its Applications
21 Linear and Multilinear Algebra
20 Applied Mathematics and Computation
10 Journal of Computational and Applied Mathematics
9 SIAM Journal on Matrix Analysis and Applications
8 Numerical Algorithms
6 Computers & Mathematics with Applications
5 International Journal of Control
5 Abstract and Applied Analysis
5 Advances in Difference Equations
4 Journal of Mathematical Analysis and Applications
4 Nonlinear Analysis. Hybrid Systems
3 Journal of the Franklin Institute
3 Journal of Optimization Theory and Applications
3 Computer Aided Geometric Design
3 Mathematical and Computer Modelling
3 MCSS. Mathematics of Control, Signals, and Systems
3 Mathematical Programming. Series A. Series B
3 Algebra Colloquium
3 ELA. The Electronic Journal of Linear Algebra
2 Computer Physics Communications
2 Journal of Computational Physics
2 Psychometrika
2 Mathematics of Computation
2 Automatica
2 Numerical Functional Analysis and Optimization
2 Numerische Mathematik
2 Journal of Symbolic Computation
2 International Journal of Computer Mathematics
2 SIAM Journal on Optimization
2 Mathematical Problems in Engineering
2 Journal of Shanghai University
2 Journal of High Energy Physics
2 Communications on Pure and Applied Analysis
2 Open Mathematics
1 Applicable Analysis
1 Bulletin of the Australian Mathematical Society
1 Communications in Mathematical Physics
1 Computer Methods in Applied Mechanics and Engineering
1 International Journal of Systems Science
1 Israel Journal of Mathematics
1 Journal of Mathematical Physics
1 Metrika
1 Ukrainian Mathematical Journal
1 Annali di Matematica Pura ed Applicata. Serie Quarta
1 Archiv der Mathematik
1 BIT
1 Czechoslovak Mathematical Journal
1 Fuzzy Sets and Systems
1 Integral Equations and Operator Theory
1 Journal of Mathematical Economics
1 Journal of Multivariate Analysis
1 Journal of Pure and Applied Algebra
1 Journal of Soviet Mathematics
1 Kyungpook Mathematical Journal
1 Proceedings of the American Mathematical Society
1 Systems & Control Letters
1 Bulletin of the Korean Mathematical Society
1 SIAM Journal on Algebraic and Discrete Methods
1 Acta Applicandae Mathematicae
1 Applied Numerical Mathematics
1 Acta Mathematicae Applicatae Sinica. English Series
1 Optimization
1 Journal of Complexity
1 Journal of Economic Dynamics & Control
1 Computational Geometry
1 Applications of Mathematics
1 Journal of Global Optimization
1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
1 Computational Statistics
1 Aequationes Mathematicae
1 Applied Mathematical Modelling
1 Automation and Remote Control
1 Communications in Partial Differential Equations
1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
1 Indagationes Mathematicae. New Series
1 Applicable Algebra in Engineering, Communication and Computing
1 Computational Optimization and Applications
1 Numerical Linear Algebra with Applications
1 Journal of the Egyptian Mathematical Society
1 Advances in Applied Clifford Algebras
1 ETNA. Electronic Transactions on Numerical Analysis
1 Journal of Difference Equations and Applications
1 Journal of Mathematical Chemistry
1 Doklady Mathematics
1 Mathematical Methods of Operations Research
1 Journal of Inequalities and Applications
1 Discrete and Continuous Dynamical Systems. Series B
1 Journal of Applied Mathematics
1 Stochastic Models
1 Journal of Applied Mathematics and Computing
1 Bulletin of the Brazilian Mathematical Society. New Series
1 Central European Journal of Mathematics
1 Fixed Point Theory and Applications
1 Journal of Control Theory and Applications
1 Statistical Methodology
1 International Journal of Number Theory
1 Advances in Data Analysis and Classification. ADAC
1 Networks and Heterogeneous Media
1 Asian-European Journal of Mathematics
...and 6 more Serials
all top 5

Cited in 48 Fields

210 Linear and multilinear algebra; matrix theory (15-XX)
134 Numerical analysis (65-XX)
35 Systems theory; control (93-XX)
30 Operator theory (47-XX)
18 Operations research, mathematical programming (90-XX)
13 Ordinary differential equations (34-XX)
11 Combinatorics (05-XX)
11 Mechanics of particles and systems (70-XX)
9 Functional analysis (46-XX)
8 Field theory and polynomials (12-XX)
8 Statistics (62-XX)
7 Algebraic geometry (14-XX)
6 Number theory (11-XX)
6 Partial differential equations (35-XX)
6 Dynamical systems and ergodic theory (37-XX)
6 Computer science (68-XX)
5 Difference and functional equations (39-XX)
4 Group theory and generalizations (20-XX)
4 Calculus of variations and optimal control; optimization (49-XX)
4 Differential geometry (53-XX)
4 Mechanics of deformable solids (74-XX)
3 Geometry (51-XX)
3 Convex and discrete geometry (52-XX)
3 Probability theory and stochastic processes (60-XX)
3 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
3 Biology and other natural sciences (92-XX)
2 Nonassociative rings and algebras (17-XX)
2 Real functions (26-XX)
2 Functions of a complex variable (30-XX)
2 Quantum theory (81-XX)
2 Statistical mechanics, structure of matter (82-XX)
2 Relativity and gravitational theory (83-XX)
2 Information and communication theory, circuits (94-XX)
1 General and overarching topics; collections (00-XX)
1 History and biography (01-XX)
1 Order, lattices, ordered algebraic structures (06-XX)
1 Commutative algebra (13-XX)
1 Associative rings and algebras (16-XX)
1 Topological groups, Lie groups (22-XX)
1 Several complex variables and analytic spaces (32-XX)
1 Special functions (33-XX)
1 Approximations and expansions (41-XX)
1 Harmonic analysis on Euclidean spaces (42-XX)
1 Integral equations (45-XX)
1 General topology (54-XX)
1 Global analysis, analysis on manifolds (58-XX)
1 Fluid mechanics (76-XX)
1 Mathematics education (97-XX)

Citations by Year