Edit Profile (opens in new tab) Sorensen, Danny C. Co-Author Distance Author ID: sorensen.danny-c Published as: Sorensen, Danny C.; Sorensen, D. C.; Sorensen, D.; Sorensen, Dan C. more...less External Links: MGP · Wikidata · GND · IdRef Documents Indexed: 88 Publications since 1978, including 5 Books 6 Contributions as Editor Biographic References: 1 Publication Co-Authors: 80 Co-Authors with 78 Joint Publications 3,592 Co-Co-Authors all top 5 Co-Authors 16 single-authored 15 Dongarra, Jack J. 7 Antoulas, Athanasios C. 4 Glowinski, Roland 4 Heinkenschloss, Matthias 4 Rojas, Marielba 3 Chaturantabut, Saifon 3 Embree, Mark 3 Hammarling, Sven J. 3 Moré, Jorge J. 3 Reichel, Lothar 3 Shah, Mili I. 3 Smith, Homer A. 3 Zhou, Yunkai 2 Ammar, Gregory S. 2 Antil, Harbir 2 Bai, Zhaojun 2 Benner, Peter 2 Bischof, Christian H. 2 Calderon, Christopher P. 2 Carroll, Raymond James 2 Demmel, James Weldon 2 Du Croz, Jeremy J. 2 Duff, Iain S. 2 Greenbaum, Anne 2 Grimme, Eric 2 Gugercin, Serkan 2 Hayes, Edward F. 2 Lehoucq, Richard B. 2 Martinez, Josue G. 2 McKenney, Alan 2 Messina, Paul F. 2 Santos, Sandra Augusta 2 Sun, Kai 2 Van der Vorst, Henk Albertus 2 Van Dooren, Paul M. 2 Voigt, Robert G. 2 Wets, Roger Jean-Baptiste 2 Yang, Chao 1 Beattie, Christopher A. 1 Blackford, S. 1 Brewer, Orlie 1 Bunch, James R. 1 Caboussat, Alexandre 1 Calvetti, Daniela 1 Castillo, Zenaida 1 Coleman, Thomas F. 1 Connolly, Kathryn 1 Darakjian, Zareh 1 Edwards, W. S. 1 Fletcher, Roger 1 Friesner, Richard A. 1 Gallivan, Kyle A. 1 Haasdonk, Bernard 1 Heath, Michael T. 1 Hoppe, Ronald H. W. 1 Jessup, Elizabeth R. 1 Kennedy, Ken 1 Klouček, Petr 1 Korombath, Prakashan P. 1 Maschhoff, Kristyn J. 1 Mehrmann, Volker 1 Nielsen, Christopher P. 1 Ohlberger, Mario 1 Oliveira, Aurelio Ribeiro Leite 1 Ostrouchov, Susan 1 Pasquali, Matteo 1 Patera, Anthony T. 1 Patterson, Jim 1 Pendergast, Phil 1 Rozza, Gianluigi 1 Sameh, Ahmed H. 1 Scroggs, Jeffrey S. 1 Tang, Ping Tak Peter 1 Tuckerman, Laurette Stephanie 1 Urban, Karsten 1 Wightman, Jennifer L. 1 Wriggers, Willy 1 Wu, Xudong T. 1 Xie, Xueying 1 Zhang, Zhiyong all top 5 Serials 6 SIAM Journal on Matrix Analysis and Applications 6 SIAM Journal on Scientific Computing 4 SIAM Journal on Numerical Analysis 4 Parallel Computing 4 Linear Algebra and its Applications 3 Journal of Computational Physics 3 ACM Transactions on Mathematical Software 3 International Journal for Numerical Methods in Engineering 3 Numerical Algorithms 3 Software - Environments - Tools 2 Mathematical Programming 2 SIAM Journal on Scientific and Statistical Computing 2 Systems & Control Letters 2 SIAM Journal on Optimization 2 ETNA. Electronic Transactions on Numerical Analysis 2 Multiscale Modeling & Simulation 2 Mathematical Programming Study 1 American Mathematical Monthly 1 Molecular Simulation 1 Applied Mathematics and Computation 1 IEEE Transactions on Computers 1 Journal of Computational and Applied Mathematics 1 Mathematical Programming Study 1 Numerische Mathematik 1 Journal of Scientific Computing 1 Journal of Non-Newtonian Fluid Mechanics 1 SIAM Review 1 Numerical Linear Algebra with Applications 1 Advances in Computational Mathematics 1 Computing and Visualization in Science 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Mathematical and Computer Modelling of Dynamical Systems 1 International Journal of Applied Mathematics and Computer Science 1 Journal of Applied Mathematics 1 Acta Numerica 1 MAA Studies in Mathematics 1 Lecture Notes in Computational Science and Engineering 1 Proceedings in Applied Mathematics all top 5 Fields 77 Numerical analysis (65-XX) 19 Linear and multilinear algebra; matrix theory (15-XX) 13 Systems theory; control (93-XX) 12 Computer science (68-XX) 12 Operations research, mathematical programming (90-XX) 11 Partial differential equations (35-XX) 6 General and overarching topics; collections (00-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 5 Statistics (62-XX) 5 Fluid mechanics (76-XX) 5 Biology and other natural sciences (92-XX) 3 Mechanics of deformable solids (74-XX) 2 History and biography (01-XX) 2 Operator theory (47-XX) 2 Probability theory and stochastic processes (60-XX) 2 Quantum theory (81-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Functions of a complex variable (30-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Approximations and expansions (41-XX) 1 Geophysics (86-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 76 Publications have been cited 4,519 times in 3,484 Documents Cited by ▼ Year ▼ LAPACK user’s guide. This work is dedicated to Jim Wilkinson. 3rd ed. Zbl 0934.65030 Anderson, E.; Bai, Z.; Bischof, C.; Blackford, S.; Demmel, J.; Dongarra, J.; Du Croz, J.; Greenbaum, A.; Hammarling, S.; McKenney, A.; Sorensen, D. 613 1999 ARPACK user’s guide. Solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods. Zbl 0901.65021 Lehoucq, R. B.; Sorensen, D. C.; Yang, C. 592 1998 Nonlinear model reduction via discrete empirical interpolation. Zbl 1217.65169 Chaturantabut, Saifon; Sorensen, Danny C. 532 2010 Computing a trust region step. Zbl 0551.65042 Moré, Jorge J.; Sorensen, D. C. 322 1983 Implicit application of polynomial filters in a \(k\)-step Arnoldi method. Zbl 0763.65025 Sorensen, Danny C. 269 1992 LAPACK user’s guide. 2nd ed. Zbl 0843.65018 Anderson, E.; Bai, Z.; Bischof, C.; Demmel, J.; Dongarra, J.; Du Croz, J.; Greenbaum, A.; Hammarling, S.; McKenney, A.; Ostrouchov, S.; Sorensen, D. 138 1995 Newton’s method with a model trust region modification. Zbl 0483.65039 Sorensen, D. C. 135 1982 Deflation techniques for an implicitly restarted Arnoldi iteration. Zbl 0863.65016 Lehoucq, R. B.; Sorensen, D. C. 131 1996 Dimension reduction of large-scale systems. Proceedings of a workshop, Oberwolfach, Germany, October 19–25, 2003. Zbl 1066.65004 120 2005 A survey of model reduction methods for large-scale systems. Zbl 1048.93014 Antoulas, A. C.; Sorensen, D. C.; Gugercin, S. 106 2001 Rank-one modification of the symmetric eigenproblem. Zbl 0369.65007 Bunch, James R.; Nielsen, Christopher P.; Sorensen, Danny C. 91 1978 Krylov methods for the incompressible Navier-Stokes equations. Zbl 0792.76062 Edwards, W. S.; Tuckerman, L. S.; Friesner, R. A.; Sorensen, Danny C. 77 1994 Numerical linear algebra for high-performance computers. Zbl 0914.65014 Dongarra, Jack J.; Duff, Iain S.; Sorensen, Danny C.; Van der Vorst, Henk A. 76 1998 On the decay rate of Hankel singular values and related issues. Zbl 1003.93024 Antoulas, A. C.; Sorensen, D. C.; Zhou, Y. 72 2002 A state space error estimate for POD-DEIM nonlinear model reduction. Zbl 1237.93035 Chaturantabut, Saifon; Sorensen, Danny C. 64 2012 A modified low-rank Smith method for large-scale Lyapunov equations. Zbl 1034.93020 Gugercin, S.; Sorensen, D. C.; Antoulas, A. C. 63 2003 The Sylvester equation and approximate balanced reduction. Zbl 1023.93012 Sorensen, D. C.; Antoulas, A. C. 61 2002 Balanced truncation model reduction for a class of descriptor systems with application to the Oseen equations. Zbl 1216.76015 Heinkenschloss, Matthias; Sorensen, Danny C.; Sun, Kai 53 2008 An implicit restarted Lanczos method for large symmetric eigenvalue problems. Zbl 0809.65030 Calvetti, D.; Reichel, L.; Sorensen, Danny C. 51 1994 A new matrix-free algorithm for the large-scale trust-region subproblem. Zbl 0994.65067 Rojas, Marielba; Santos, Sandra A.; Sorensen, Danny C. 51 2000 On the use of directions of negative curvature in a modified Newton method. Zbl 0394.90093 More, Jorge J.; Sorensen, Danny C. 49 1979 Model reduction of state space systems via an implicitly restarted Lanczos method. Zbl 0870.65052 Grimme, E. J.; Sorensen, D. C.; Van Dooren, P. 47 1996 A new class of preconditioners for large-scale linear systems from interior point methods for linear programming. Zbl 1071.65088 Oliveira, A. R. L.; Sorensen, D. C. 44 2005 Application of POD and DEIM on dimension reduction of non-linear miscible viscous fingering in porous media. Zbl 1302.76127 Chaturantabut, Saifon; Sorensen, Danny C. 40 2011 A posteriori error estimation for DEIM reduced nonlinear dynamical systems. Zbl 1312.65127 Wirtz, D.; Sorensen, D. C.; Haasdonk, B. 38 2014 Minimization of a large-scale quadratic function subject to a spherical constraint. Zbl 0878.65044 Sorensen, D. C. 37 1997 Approximation of large-scale dynamical systems: An overview. Zbl 1024.93008 Antoulas, Athanasios C.; Sorensen, Dan C. 37 2001 The Q-superlinear convergence of a collinear scaling algorithm for unconstrained optimization. Zbl 0428.65040 Sorensen, D. C. 37 1980 Passivity preserving model reduction via interpolation of spectral zeros. Zbl 1129.93340 Sorensen, D. C. 36 2005 A DEIM induced CUR factorization. Zbl 1382.65121 Sorensen, D. C.; Embree, Mark 34 2016 Numerical methods for large eigenvalue problems. Zbl 1105.65325 Sorensen, Danny C. 31 2002 A fully parallel algorithm for the symmetric eigenvalue problem. Zbl 0627.65033 Dongarra, Jack J.; Sorensen, Danny C. 30 1987 Algorithm 873: LSTRS: MATLAB software for large-scale trust-region subproblems and regularization. Zbl 1291.65177 Rojas, Marielba; Santos, Sandra A.; Sorensen, Danny C. 30 2008 A trust-region approach to the regularization of large-scale discrete forms of ill-posed problems. Zbl 1006.86004 Rojas, Marielba; Sorensen, Danny C. 29 2002 Implicitly restarted Arnoldi/Lanczos methods for large scale eigenvalue calculations. Zbl 0865.65019 Sorensen, Danny C. 26 1997 Direct methods for matrix Sylvester and Lyapunov equations. Zbl 1028.65039 Sorensen, Danny C.; Zhou, Yunkai 24 2003 Domain decomposition and model reduction for the numerical solution of PDE constrained optimization problems with localized optimization variables. Zbl 1220.65074 Antil, Harbir; Heinkenschloss, Matthias; Hoppe, Ronald H. W.; Sorensen, Danny C. 22 2010 Convergence of polynomial restart Krylov methods for eigenvalue computations. Zbl 1073.65028 Beattie, Christopher A.; Embree, Mark; Sorensen, D. C. 20 2005 A least-squares method for the numerical solution of the Dirichlet problem for the elliptic Monge-Ampère equation in dimension two. Zbl 1272.65089 Caboussat, Alexandre; Glowinski, Roland; Sorensen, Danny C. 20 2013 P_ARPACK: An efficient portable large scale eigenvalue package for distributed memory parallel architectures. Zbl 0886.65034 Maschhoff, K. J.; Sorensen, D. C. 17 1996 Block reduction of matrices to condensed forms for eigenvalue computations. Zbl 0679.65025 Dongarra, Jack J.; Sorensen, Danny C.; Hammarling, Sven J. 17 1989 On the orthogonality of eigenvectors computed by divide-and-conquer techniques. Zbl 0743.65039 Sorensen, Danny C.; Tang, Ping Tak Peter 16 1991 Application of the discrete empirical interpolation method to reduced order modeling of nonlinear and parametric systems. Zbl 1312.65180 Antil, Harbir; Heinkenschloss, Matthias; Sorensen, Danny C. 16 2014 A note on the computation of an orthonormal basis for the null space of a matrix. Zbl 0539.65020 Coleman, Thomas F.; Sorensen, Danny C. 16 1984 Solving linear systems on vector and shared memory computers. Zbl 0770.65009 Dongarra, Jack J.; Duff, Iain S.; Sorensen, Danny C.; Van der Vorst, Henk A. 15 1990 An implementation of a divide and conquer algorithm for the unitary eigenproblem. Zbl 0892.65025 Ammar, G. S.; Reichel, L.; Sorensen, D. C. 15 1992 Newton’s method. Zbl 0608.65037 Moré, Jorge J.; Sorensen, Danny C. 15 1984 Accelerating the LSTRS algorithm. Zbl 1368.65096 Lampe, J.; Rojas, M.; Sorensen, D. C.; Voss, H. 13 2011 A truncated RQ iteration for large scale eigenvalue calculations. Zbl 0918.65023 Sorensen, D. C.; Yang, C. 10 1998 Analysis of pairwise pivoting in Gaussian elimination. Zbl 0551.65014 Sorensen, Danny C. 10 1985 A parallel algorithm for computing the singular value decomposition of a matrix. Zbl 0797.65037 Jessup, E. R.; Sorensen, Danny C. 9 1994 Collinear scaling and sequential estimation in sparse optimization algorithms. Zbl 0508.49028 Sorensen, D. C. 9 1982 The approximation and computation of a basis of the trace space \(H^{1/2}\). Zbl 1122.65119 Klouček, Petr; Sorensen, Danny C.; Wightman, Jennifer L. 8 2007 Implementation of some concurrent algorithms for matrix factorization. Zbl 0591.65027 Dongarra, J. J.; Sameh, A. H.; Sorensen, D. C. 7 1986 On model reduction of structured systems. Zbl 1103.93018 Sorensen, Danny C.; Antoulas, Athanasios C. 7 2005 Computing the eigenvalues of the Laplace-Beltrami operator on the surface of a torus: a numerical approach. Zbl 1152.65477 Glowinski, Roland; Sorensen, Danny C. 7 2008 Implicitly restarted Arnoldi/Lanczos methods and large scale SVD applications. Zbl 0826.65036 Sorensen, D. C. 6 1995 Corrigendum: Algorithm 730. An implementation of a divide and conquer algorithm for the unitary eigenproblem. Zbl 0894.65017 Ammar, G. S.; Reichel, L.; Sorensen, D. C. 6 1994 A quadratically constrained minimization problem arising from PDE of Monge-Ampère type. Zbl 1187.65073 Sorensen, Danny C.; Glowinski, Roland 6 2010 Linear algebra on high performance computers. Zbl 0628.65016 Dongarra, Jack J.; Sorensen, Danny C. 5 1986 Approximate implicit subspace iteration with alternating directions for LTI system model reduction. Zbl 1212.65258 Zhou, Y.; Sorensen, D. C. 5 2008 Formulation and solution of the nonlinear, damped eigenvalue problem for skeletal systems. Zbl 0848.73039 Smith, H. A.; Singh, R. K.; Sorensen, D. C. 4 1995 An algorithmic derivation of the Jordan canonical form. Zbl 0529.15008 Fletcher, R.; Sorensen, D. C. 4 1983 Trust region methods for unconstrained minimization. Zbl 0571.90081 Sorensen, D. C. 4 1982 Domain decomposition and model reduction of systems with local nonlinearities. Zbl 1157.65445 Sun, K.; Glowinski, R.; Heinkenschloss, M.; Sorensen, D. C. 4 2008 On some modifications of the Lanczos algorithm and the relation with Padé approximations. Zbl 1075.93506 Gallivan, K.; Grimme, E.; Sorensen, D.; Van Dooren, P. 3 1996 A Lanczos-based technique for exact vibration analysis of skeletal structures. Zbl 0775.73152 Smith, H. A.; Sorensen, Danny C.; Singh, R. K. 3 1993 Lyapunov, Lanczos, and inertia. Zbl 0997.65065 Antoulas, A. C.; Sorensen, D. C. 2 2001 A pipelined Givens method for computing the QR factorization of a sparse matrix. Zbl 0587.65018 Heath, M. T.; Sorensen, D. C. 2 1986 Truncated \(QZ\) methods for large scale generalized eigenvalue problems. Zbl 0915.65028 Sorensen, D. C. 2 1998 Buffering for vector performance on a pipelined MIMD machine. Zbl 0547.65036 Sorensen, D. C. 2 1984 A symmetry preserving singular value decomposition. Zbl 1124.65042 Shah, Mili I.; Sorensen, Danny C. 2 2006 Parallel solution of large-scale free surface viscoelastic flows via sparse approximate inverse preconditioning. Zbl 1274.76095 Castillo, Zenaida; Xie, Xueying; Sorensen, Danny C.; Embree, Mark; Pasquali, Matteo 1 2009 Programming methodology and performance issues for advanced computer architectures. Zbl 0656.68035 Dongarra, Jack J.; Sorensen, Danny C.; Connolly, Kathryn; Patterson, Jim 1 1988 Best nonspherical symmetric low rank approximation. Zbl 1201.65065 Shah, Mili I.; Sorensen, Danny C. 1 2010 A parameter free ADI-like method for the numerical solution of large scale Lyapunov equations. Zbl 1372.65131 Sorensen, Danny C. 1 2016 A DEIM induced CUR factorization. Zbl 1382.65121 Sorensen, D. C.; Embree, Mark 34 2016 A parameter free ADI-like method for the numerical solution of large scale Lyapunov equations. Zbl 1372.65131 Sorensen, Danny C. 1 2016 A posteriori error estimation for DEIM reduced nonlinear dynamical systems. Zbl 1312.65127 Wirtz, D.; Sorensen, D. C.; Haasdonk, B. 38 2014 Application of the discrete empirical interpolation method to reduced order modeling of nonlinear and parametric systems. Zbl 1312.65180 Antil, Harbir; Heinkenschloss, Matthias; Sorensen, Danny C. 16 2014 A least-squares method for the numerical solution of the Dirichlet problem for the elliptic Monge-Ampère equation in dimension two. Zbl 1272.65089 Caboussat, Alexandre; Glowinski, Roland; Sorensen, Danny C. 20 2013 A state space error estimate for POD-DEIM nonlinear model reduction. Zbl 1237.93035 Chaturantabut, Saifon; Sorensen, Danny C. 64 2012 Application of POD and DEIM on dimension reduction of non-linear miscible viscous fingering in porous media. Zbl 1302.76127 Chaturantabut, Saifon; Sorensen, Danny C. 40 2011 Accelerating the LSTRS algorithm. Zbl 1368.65096 Lampe, J.; Rojas, M.; Sorensen, D. C.; Voss, H. 13 2011 Nonlinear model reduction via discrete empirical interpolation. Zbl 1217.65169 Chaturantabut, Saifon; Sorensen, Danny C. 532 2010 Domain decomposition and model reduction for the numerical solution of PDE constrained optimization problems with localized optimization variables. Zbl 1220.65074 Antil, Harbir; Heinkenschloss, Matthias; Hoppe, Ronald H. W.; Sorensen, Danny C. 22 2010 A quadratically constrained minimization problem arising from PDE of Monge-Ampère type. Zbl 1187.65073 Sorensen, Danny C.; Glowinski, Roland 6 2010 Best nonspherical symmetric low rank approximation. Zbl 1201.65065 Shah, Mili I.; Sorensen, Danny C. 1 2010 Parallel solution of large-scale free surface viscoelastic flows via sparse approximate inverse preconditioning. Zbl 1274.76095 Castillo, Zenaida; Xie, Xueying; Sorensen, Danny C.; Embree, Mark; Pasquali, Matteo 1 2009 Balanced truncation model reduction for a class of descriptor systems with application to the Oseen equations. Zbl 1216.76015 Heinkenschloss, Matthias; Sorensen, Danny C.; Sun, Kai 53 2008 Algorithm 873: LSTRS: MATLAB software for large-scale trust-region subproblems and regularization. Zbl 1291.65177 Rojas, Marielba; Santos, Sandra A.; Sorensen, Danny C. 30 2008 Computing the eigenvalues of the Laplace-Beltrami operator on the surface of a torus: a numerical approach. Zbl 1152.65477 Glowinski, Roland; Sorensen, Danny C. 7 2008 Approximate implicit subspace iteration with alternating directions for LTI system model reduction. Zbl 1212.65258 Zhou, Y.; Sorensen, D. C. 5 2008 Domain decomposition and model reduction of systems with local nonlinearities. Zbl 1157.65445 Sun, K.; Glowinski, R.; Heinkenschloss, M.; Sorensen, D. C. 4 2008 The approximation and computation of a basis of the trace space \(H^{1/2}\). Zbl 1122.65119 Klouček, Petr; Sorensen, Danny C.; Wightman, Jennifer L. 8 2007 A symmetry preserving singular value decomposition. Zbl 1124.65042 Shah, Mili I.; Sorensen, Danny C. 2 2006 Dimension reduction of large-scale systems. Proceedings of a workshop, Oberwolfach, Germany, October 19–25, 2003. Zbl 1066.65004 120 2005 A new class of preconditioners for large-scale linear systems from interior point methods for linear programming. Zbl 1071.65088 Oliveira, A. R. L.; Sorensen, D. C. 44 2005 Passivity preserving model reduction via interpolation of spectral zeros. Zbl 1129.93340 Sorensen, D. C. 36 2005 Convergence of polynomial restart Krylov methods for eigenvalue computations. Zbl 1073.65028 Beattie, Christopher A.; Embree, Mark; Sorensen, D. C. 20 2005 On model reduction of structured systems. Zbl 1103.93018 Sorensen, Danny C.; Antoulas, Athanasios C. 7 2005 A modified low-rank Smith method for large-scale Lyapunov equations. Zbl 1034.93020 Gugercin, S.; Sorensen, D. C.; Antoulas, A. C. 63 2003 Direct methods for matrix Sylvester and Lyapunov equations. Zbl 1028.65039 Sorensen, Danny C.; Zhou, Yunkai 24 2003 On the decay rate of Hankel singular values and related issues. Zbl 1003.93024 Antoulas, A. C.; Sorensen, D. C.; Zhou, Y. 72 2002 The Sylvester equation and approximate balanced reduction. Zbl 1023.93012 Sorensen, D. C.; Antoulas, A. C. 61 2002 Numerical methods for large eigenvalue problems. Zbl 1105.65325 Sorensen, Danny C. 31 2002 A trust-region approach to the regularization of large-scale discrete forms of ill-posed problems. Zbl 1006.86004 Rojas, Marielba; Sorensen, Danny C. 29 2002 A survey of model reduction methods for large-scale systems. Zbl 1048.93014 Antoulas, A. C.; Sorensen, D. C.; Gugercin, S. 106 2001 Approximation of large-scale dynamical systems: An overview. Zbl 1024.93008 Antoulas, Athanasios C.; Sorensen, Dan C. 37 2001 Lyapunov, Lanczos, and inertia. Zbl 0997.65065 Antoulas, A. C.; Sorensen, D. C. 2 2001 A new matrix-free algorithm for the large-scale trust-region subproblem. Zbl 0994.65067 Rojas, Marielba; Santos, Sandra A.; Sorensen, Danny C. 51 2000 LAPACK user’s guide. This work is dedicated to Jim Wilkinson. 3rd ed. Zbl 0934.65030 Anderson, E.; Bai, Z.; Bischof, C.; Blackford, S.; Demmel, J.; Dongarra, J.; Du Croz, J.; Greenbaum, A.; Hammarling, S.; McKenney, A.; Sorensen, D. 613 1999 ARPACK user’s guide. Solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods. Zbl 0901.65021 Lehoucq, R. B.; Sorensen, D. C.; Yang, C. 592 1998 Numerical linear algebra for high-performance computers. Zbl 0914.65014 Dongarra, Jack J.; Duff, Iain S.; Sorensen, Danny C.; Van der Vorst, Henk A. 76 1998 A truncated RQ iteration for large scale eigenvalue calculations. Zbl 0918.65023 Sorensen, D. C.; Yang, C. 10 1998 Truncated \(QZ\) methods for large scale generalized eigenvalue problems. Zbl 0915.65028 Sorensen, D. C. 2 1998 Minimization of a large-scale quadratic function subject to a spherical constraint. Zbl 0878.65044 Sorensen, D. C. 37 1997 Implicitly restarted Arnoldi/Lanczos methods for large scale eigenvalue calculations. Zbl 0865.65019 Sorensen, Danny C. 26 1997 Deflation techniques for an implicitly restarted Arnoldi iteration. Zbl 0863.65016 Lehoucq, R. B.; Sorensen, D. C. 131 1996 Model reduction of state space systems via an implicitly restarted Lanczos method. Zbl 0870.65052 Grimme, E. J.; Sorensen, D. C.; Van Dooren, P. 47 1996 P_ARPACK: An efficient portable large scale eigenvalue package for distributed memory parallel architectures. Zbl 0886.65034 Maschhoff, K. J.; Sorensen, D. C. 17 1996 On some modifications of the Lanczos algorithm and the relation with Padé approximations. Zbl 1075.93506 Gallivan, K.; Grimme, E.; Sorensen, D.; Van Dooren, P. 3 1996 LAPACK user’s guide. 2nd ed. Zbl 0843.65018 Anderson, E.; Bai, Z.; Bischof, C.; Demmel, J.; Dongarra, J.; Du Croz, J.; Greenbaum, A.; Hammarling, S.; McKenney, A.; Ostrouchov, S.; Sorensen, D. 138 1995 Implicitly restarted Arnoldi/Lanczos methods and large scale SVD applications. Zbl 0826.65036 Sorensen, D. C. 6 1995 Formulation and solution of the nonlinear, damped eigenvalue problem for skeletal systems. Zbl 0848.73039 Smith, H. A.; Singh, R. K.; Sorensen, D. C. 4 1995 Krylov methods for the incompressible Navier-Stokes equations. Zbl 0792.76062 Edwards, W. S.; Tuckerman, L. S.; Friesner, R. A.; Sorensen, Danny C. 77 1994 An implicit restarted Lanczos method for large symmetric eigenvalue problems. Zbl 0809.65030 Calvetti, D.; Reichel, L.; Sorensen, Danny C. 51 1994 A parallel algorithm for computing the singular value decomposition of a matrix. Zbl 0797.65037 Jessup, E. R.; Sorensen, Danny C. 9 1994 Corrigendum: Algorithm 730. An implementation of a divide and conquer algorithm for the unitary eigenproblem. Zbl 0894.65017 Ammar, G. S.; Reichel, L.; Sorensen, D. C. 6 1994 A Lanczos-based technique for exact vibration analysis of skeletal structures. Zbl 0775.73152 Smith, H. A.; Sorensen, Danny C.; Singh, R. K. 3 1993 Implicit application of polynomial filters in a \(k\)-step Arnoldi method. Zbl 0763.65025 Sorensen, Danny C. 269 1992 An implementation of a divide and conquer algorithm for the unitary eigenproblem. Zbl 0892.65025 Ammar, G. S.; Reichel, L.; Sorensen, D. C. 15 1992 On the orthogonality of eigenvectors computed by divide-and-conquer techniques. Zbl 0743.65039 Sorensen, Danny C.; Tang, Ping Tak Peter 16 1991 Solving linear systems on vector and shared memory computers. Zbl 0770.65009 Dongarra, Jack J.; Duff, Iain S.; Sorensen, Danny C.; Van der Vorst, Henk A. 15 1990 Block reduction of matrices to condensed forms for eigenvalue computations. Zbl 0679.65025 Dongarra, Jack J.; Sorensen, Danny C.; Hammarling, Sven J. 17 1989 Programming methodology and performance issues for advanced computer architectures. Zbl 0656.68035 Dongarra, Jack J.; Sorensen, Danny C.; Connolly, Kathryn; Patterson, Jim 1 1988 A fully parallel algorithm for the symmetric eigenvalue problem. Zbl 0627.65033 Dongarra, Jack J.; Sorensen, Danny C. 30 1987 Implementation of some concurrent algorithms for matrix factorization. Zbl 0591.65027 Dongarra, J. J.; Sameh, A. H.; Sorensen, D. C. 7 1986 Linear algebra on high performance computers. Zbl 0628.65016 Dongarra, Jack J.; Sorensen, Danny C. 5 1986 A pipelined Givens method for computing the QR factorization of a sparse matrix. Zbl 0587.65018 Heath, M. T.; Sorensen, D. C. 2 1986 Analysis of pairwise pivoting in Gaussian elimination. Zbl 0551.65014 Sorensen, Danny C. 10 1985 A note on the computation of an orthonormal basis for the null space of a matrix. Zbl 0539.65020 Coleman, Thomas F.; Sorensen, Danny C. 16 1984 Newton’s method. Zbl 0608.65037 Moré, Jorge J.; Sorensen, Danny C. 15 1984 Buffering for vector performance on a pipelined MIMD machine. Zbl 0547.65036 Sorensen, D. C. 2 1984 Computing a trust region step. Zbl 0551.65042 Moré, Jorge J.; Sorensen, D. C. 322 1983 An algorithmic derivation of the Jordan canonical form. Zbl 0529.15008 Fletcher, R.; Sorensen, D. C. 4 1983 Newton’s method with a model trust region modification. Zbl 0483.65039 Sorensen, D. C. 135 1982 Collinear scaling and sequential estimation in sparse optimization algorithms. Zbl 0508.49028 Sorensen, D. C. 9 1982 Trust region methods for unconstrained minimization. Zbl 0571.90081 Sorensen, D. C. 4 1982 The Q-superlinear convergence of a collinear scaling algorithm for unconstrained optimization. Zbl 0428.65040 Sorensen, D. C. 37 1980 On the use of directions of negative curvature in a modified Newton method. Zbl 0394.90093 More, Jorge J.; Sorensen, Danny C. 49 1979 Rank-one modification of the symmetric eigenproblem. Zbl 0369.65007 Bunch, James R.; Nielsen, Christopher P.; Sorensen, Danny C. 91 1978 all cited Publications top 5 cited Publications all top 5 Cited by 5,454 Authors 92 Benner, Peter 34 Reichel, Lothar 27 Gugercin, Serkan 23 Willcox, Karen E. 22 Kressner, Daniel 22 Navon, Ionel Michael 21 Hesthaven, Jan S. 21 Manzoni, Andrea 19 Beattie, Christopher A. 19 Mehrmann, Volker 19 Simoncini, Valeria 18 Zhu, Detong 17 Schmid, Peter Joseph 17 Zhang, Lei-Hong 16 Dongarra, Jack J. 16 Meerbergen, Karl 16 Quarteroni, Alfio M. 16 Quintana-Ortí, Enrique S. 16 Sipp, Denis 15 Carlberg, Kevin T. 15 Farhat, Charbel H. 15 Jia, Zhongxiao 15 Li, Rencang 15 Oliveira, Aurelio Ribeiro Leite 15 Peherstorfer, Benjamin 15 Sorensen, Danny C. 15 Stykel, Tatjana 15 Wu, Gang 14 Fang, Fangxin 14 Giani, Stefano 14 Karasözen, Bülent 14 Saak, Jens 13 Antoulas, Athanasios C. 13 Calvetti, Daniela 13 Dehghan Takht Fooladi, Mehdi 13 Feng, Lihong 13 Haasdonk, Bernard 13 Heinkenschloss, Matthias 13 Jbilou, Khalide 13 Lin, Wen-Wei 13 Saad, Yousef 13 Sun, Wenyu 13 Uzunca, Murat 12 Drmač, Zlatko 12 Martínez, José Mario 12 Pain, Christopher C. 12 Pini, Giorgio 12 Rozza, Gianluigi 12 Van Dooren, Paul M. 11 Abbaszadeh, Mostafa 11 Breiten, Tobias 11 Brunton, Steven L. 11 Goyal, Pawan 11 Jiang, Yaolin 11 Wei, Yimin 11 Xia, Yong 10 Baglama, James 10 Bergamaschi, Luca 10 Glowinski, Roland 10 Golub, Gene Howard 10 Heiland, Jan 10 Heltai, Luca 10 Higham, Nicholas J. 10 Hochstenbach, Michiel E. 10 Kürschner, Patrick 10 Yang, Chao 10 Zhou, Yunkai 10 Zlatev, Zahari 9 Abdel-Aziz, Mohammedi R. 9 Aishima, Kensuke 9 Alla, Alessandro 9 Amsallem, David 9 Bai, Zhaojun 9 Bangerth, Wolfgang 9 Caboussat, Alexandre 9 Chaturantabut, Saifon 9 Choi, Youngsoo 9 Chomaz, Jean-Marc 9 Faßbender, Heike 9 Gondzio, Jacek 9 Heister, Timo 9 Henningson, Dan S. 9 Iliescu, Traian 9 Kronbichler, Martin 9 Kutz, J. Nathan 9 Maier, Matthias Sebastian 9 Ni, Qin 9 Qu, Shaojian 9 Shen, Chungen 9 Turcksin, Bruno 8 Ariyawansa, K. A. 8 Arndt, Daniel 8 Embree, Mark 8 Himpe, Christian 8 Lu, Linzhang 8 Lukšan, Ladislav 8 Marquet, Olivier 8 Pelteret, Jean-Paul 8 Quintana-Ortí, Gregorio 8 Robinet, Jean-Christophe ...and 5,354 more Authors all top 5 Cited in 380 Serials 214 Journal of Computational Physics 174 Journal of Computational and Applied Mathematics 159 SIAM Journal on Scientific Computing 157 Computer Methods in Applied Mechanics and Engineering 141 Linear Algebra and its Applications 121 Journal of Fluid Mechanics 88 Applied Mathematics and Computation 81 Computer Physics Communications 74 Computers & Mathematics with Applications 73 International Journal for Numerical Methods in Engineering 73 SIAM Journal on Matrix Analysis and Applications 64 Journal of Scientific Computing 64 Numerical Algorithms 59 Numerical Linear Algebra with Applications 58 Mathematical Programming. Series A. Series B 57 Computational Optimization and Applications 55 Applied Numerical Mathematics 48 Optimization Methods & Software 45 Numerische Mathematik 42 Computers and Fluids 41 BIT 41 Journal of Optimization Theory and Applications 41 Advances in Computational Mathematics 32 SIAM Journal on Optimization 31 Systems & Control Letters 28 Automatica 28 Computational Mechanics 27 Mathematics of Computation 27 Physics of Fluids 21 International Journal for Numerical Methods in Fluids 21 Journal of Global Optimization 19 Mathematics and Computers in Simulation 19 Engineering Analysis with Boundary Elements 17 European Journal of Operational Research 16 Computing 16 Mathematical and Computer Modelling 16 Mathematical and Computer Modelling of Dynamical Systems 15 ACM Transactions on Mathematical Software 15 International Journal of Computer Mathematics 14 Optimization 14 Applied Mathematics Letters 14 Applied Mathematical Modelling 14 Computational Geosciences 13 Computational and Applied Mathematics 13 Acta Numerica 13 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 12 International Journal of Control 12 Journal of the Franklin Institute 12 Physica D 11 Linear and Multilinear Algebra 11 Mathematical Programming 11 Japan Journal of Industrial and Applied Mathematics 11 ETNA. Electronic Transactions on Numerical Analysis 11 European Journal of Mechanics. B. Fluids 11 Journal of Numerical Mathematics 11 Optimization Letters 11 SIAM/ASA Journal on Uncertainty Quantification 10 Numerical Functional Analysis and Optimization 10 SIAM Journal on Numerical Analysis 10 Annals of Operations Research 10 Mathematical Problems in Engineering 10 Multiscale Modeling & Simulation 9 Calcolo 9 International Journal of Computational Fluid Dynamics 9 Archives of Computational Methods in Engineering 9 Journal of Machine Learning Research (JMLR) 9 GAMM-Mitteilungen 9 Communications in Computational Physics 9 Mathematical Programming Computation 9 Numerical Algebra, Control and Optimization 8 SIAM Journal on Control and Optimization 8 Computational Statistics and Data Analysis 7 Inverse Problems 7 Parallel Computing 7 MCSS. Mathematics of Control, Signals, and Systems 7 SIAM Review 7 Communications in Numerical Methods in Engineering 7 Chaos 7 European Journal of Mechanics. A. Solids 7 SIAM Journal on Applied Dynamical Systems 7 SIAM Journal on Imaging Sciences 7 Statistics and Computing 7 International Journal of Systems Science. Principles and Applications of Systems and Integration 6 Mathematical Biosciences 6 Machine Learning 6 Journal of Nonlinear Science 6 Journal of Mathematical Chemistry 6 European Journal of Control 6 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 6 Vestnik Samarskogo Universiteta. Estestvennonauchnaya Seriya 5 Acta Mechanica 5 Journal of Mathematical Physics 5 Applied Mathematics and Optimization 5 Kybernetika 5 Operations Research Letters 5 Computer Aided Geometric Design 5 COMPEL 5 Numerical Methods for Partial Differential Equations 5 Annals of Physics 5 Computing and Visualization in Science ...and 280 more Serials all top 5 Cited in 54 Fields 2,162 Numerical analysis (65-XX) 579 Operations research, mathematical programming (90-XX) 568 Fluid mechanics (76-XX) 427 Linear and multilinear algebra; matrix theory (15-XX) 372 Partial differential equations (35-XX) 367 Systems theory; control (93-XX) 246 Mechanics of deformable solids (74-XX) 206 Computer science (68-XX) 176 Calculus of variations and optimal control; optimization (49-XX) 153 Statistics (62-XX) 120 Optics, electromagnetic theory (78-XX) 109 Quantum theory (81-XX) 102 Dynamical systems and ergodic theory (37-XX) 99 Statistical mechanics, structure of matter (82-XX) 85 Ordinary differential equations (34-XX) 85 Biology and other natural sciences (92-XX) 57 Approximations and expansions (41-XX) 52 Probability theory and stochastic processes (60-XX) 50 Geophysics (86-XX) 47 Classical thermodynamics, heat transfer (80-XX) 44 Operator theory (47-XX) 41 Mechanics of particles and systems (70-XX) 35 Information and communication theory, circuits (94-XX) 27 Combinatorics (05-XX) 20 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 15 Functions of a complex variable (30-XX) 15 Integral equations (45-XX) 14 Real functions (26-XX) 14 Harmonic analysis on Euclidean spaces (42-XX) 14 Global analysis, analysis on manifolds (58-XX) 11 Differential geometry (53-XX) 8 Algebraic geometry (14-XX) 8 Difference and functional equations (39-XX) 7 Potential theory (31-XX) 7 Functional analysis (46-XX) 7 Astronomy and astrophysics (85-XX) 6 Field theory and polynomials (12-XX) 6 Relativity and gravitational theory (83-XX) 5 Number theory (11-XX) 5 Special functions (33-XX) 4 General and overarching topics; collections (00-XX) 4 History and biography (01-XX) 3 Convex and discrete geometry (52-XX) 3 Mathematics education (97-XX) 2 Mathematical logic and foundations (03-XX) 2 Commutative algebra (13-XX) 2 Sequences, series, summability (40-XX) 2 Integral transforms, operational calculus (44-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Geometry (51-XX) 1 Algebraic topology (55-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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