×

A mathematical biography of Danny C. Sorensen. (English) Zbl 1238.01104

Summary: On the occasion of his 65th birthday, we briefly recount Dan Sorensen’s profound contributions to optimization, numerical linear algebra, and model order reduction for dynamical systems.

MSC:

01A70 Biographies, obituaries, personalia, bibliographies

Biographic References:

Sorensen, Danny C.
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Anderson, E.; Bai, Z.; Bischof, C.; Blackford, S.; Demmel, J.; Dongarra, J.; Du Croz, J.; Greenbaum, A.; Hammarling, S.; McKenney, A.; Sorensen, D., LAPACK User’s Guide (1999), SIAM: SIAM Philadelphia · Zbl 0934.65030
[2] Anderson, E.; Bai, Z.; Bischof, C.; Demmel, J.; Dongarra, J.; Croz, J. D.; Greenbaum, A.; Hammarling, S.; McKenney, A.; Ostrou- chov, S.; Sorensen, D., LAPACK Users Guide (1992), SIAM: SIAM Philadelphia
[3] Antoulas, A. C., A new result on passivity preserving model reduction, Systems Control Lett., 54, 361-374 (2005) · Zbl 1129.93304
[4] Antoulas, A. C., Approximation of Large-Scale Dynamical Systems (2005), SIAM: SIAM Philadelphia · Zbl 1112.93002
[5] Antoulas, A. C.; Sorensen, D. C.; Gugercin, S., A survey of model reduction methods for large-scale systems, (Contemporary Mathematics, vol. 280 (2001), American Mathematical Society: American Mathematical Society Providence, RI), 193-219 · Zbl 1048.93014
[6] Antoulas, A. C.; Sorensen, D. C.; Zhou, Y., On the decay rate of Hankel singular values and related issues, Systems Control Lett., 46, 323-342 (2002) · Zbl 1003.93024
[7] Arnoldi, W. E., The principle of minimized iterations in the solution of the matrix eigenvalue problem, Quart. Appl. Math., 9, 17-29 (1951) · Zbl 0042.12801
[8] Barrault, M.; Maday, Y.; Nguyen, N.; Patera, A. T., An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations, C. R. Acad. Sci. Paris Ser. I, 339, 667-672 (2004) · Zbl 1061.65118
[9] Beattie, C. A.; Embree, M.; Sorensen, D. C., Convergence of polynomial restart Krylov methods for eigenvalue computations, SIAM Rev., 47, 492-515 (2005) · Zbl 1073.65028
[10] Benner, P.; Freund, R.; Sorensen, D.; Varga, A., Preface special issue on order reduction of large-scale systems, Linear Algebra Appl., 415, 231-234 (2006)
[11] (Benner, P.; Mehrmann, V.; Sorensen, D. C., Dimension Reduction of Large-Scale Systems. Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, vol. 5 (2005), Springer-Verlag: Springer-Verlag Berlin/Heidelberg, Germany) · Zbl 1066.65004
[12] Benner, P.; Quintana-Orti, E. S.; Quintana-Orti, G., Balanced truncation model reduction of large-scale dense systems on parallel computers, Math. Comput. Model. Dyn. Syst., 6, 383-405 (2000) · Zbl 0978.93013
[13] Bunch, J. R.; Nielsen, C. P.; Sorensen, D. C., Rank-one modification of the symmetric eigenproblem, Numer. Math., 31, 31-48 (1978) · Zbl 0369.65007
[14] Calvetti, D.; Reichel, L.; Sorensen, D. C., An implicitly restarted Lanczos method for large symmetric eigenvalue problems, Electron. Trans. Numer. Anal., 2, 1-21 (1994) · Zbl 0809.65030
[15] Chaturantabut, S.; Sorensen, D. C., Nonlinear model reduction via discrete empirical interpolation, SIAM J. Sci. Comput., 32, 2737-2764 (2010) · Zbl 1217.65169
[16] Chaturantabut, S.; Sorensen, D. C., Application of POD and DEIM on dimension reduction of non-linear miscible viscous fingering in porous media, Math. Comput. Model. Dyn. Syst., 17, 337-353 (2011) · Zbl 1302.76127
[17] Cuppen, J. J.M., A divide and conquer method for the symmetric tridiagonal eigenproblem, Numer. Math., 36, 177-195 (1981) · Zbl 0431.65022
[18] Daniel, J.; Gragg, W. B.; Kaufman, L.; Stewart, G. W., Re-orthogonalization and stable algorithms for updating the Gram-Schmidt QR factorization, Math. Comput., 30, 772-795 (1976) · Zbl 0345.65021
[19] Dongarra, J. J.; Duff, I. S.; Sorensen, D. C.; van der Vorst, H., Solving Linear Systems on Vector and Shared Memory Computers (1990), SIAM: SIAM Philadelphia · Zbl 0770.65009
[20] Dongarra, J. J.; Duff, I. S.; Sorensen, D. C.; van der Vorst, H., Solving Linear Systems on Vector and Shared Memory Computers (1991), SIAM: SIAM Philadelphia
[21] Dongarra, J. J.; Duff, I. S.; Sorensen, D. C.; van der Vorst, H., Numerical Linear Algebra for High-Performance Computers (1998), SIAM: SIAM Philadelphia · Zbl 0914.65014
[22] Dongarra, J. J.; Sorensen, D. C., A fully parallel algorithm for the symmetric eigenvalue problem, SIAM J. Sci. Statist. Comput., 8, s139-s154 (1987) · Zbl 0627.65033
[23] Dongarra, J. J.; Sorensen, D. C.; Hammarling, S. J., Block reduction of matrices to condensed forms for eigenvalue computations, J. Comput. Appl. Math., 27, 215-227 (1987) · Zbl 0679.65025
[24] Feldmann, P.; Freund, R. W., Efficient linear circuit analysis by Padé approximation via the Lanczos process, (Proceedings of EURO-DAC ’94 with EURO-VHDL ’94, Grenoble, France (1994), IEEE Computer Society Press), 170-175
[25] Feldmann, P.; Freund, R. W., Efficient linear circuit analysis by Padé approximation via the Lanczos process, IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., 14, 639-649 (1995)
[26] Freund, R., Model reduction methods based on Krylov subspaces, Acta Numer., 12, 267-319 (2003) · Zbl 1046.65021
[27] Gallivan, K.; Grimme, E.; Van Dooren, P., Asymptotic waveform evaluation via a Lanczos method, Appl. Math. Lett., 7, 75-80 (1994) · Zbl 0810.65067
[28] Golub, G. H., Some modified matrix eigenvalue problems, SIAM Rev., 15, 318-334 (1973) · Zbl 0254.65027
[29] Grimme, E. J.; Sorensen, D. C.; van Dooren, P., Model reduction of state space systems via an implicitly restarted Lanczos method, Numer. Algorithms, 12, 1-31 (1995) · Zbl 0870.65052
[30] Gu, M.; Eisenstat, S. C., A divide-and-conquer algorithm for the symmetric tridiagonal eigenproblem, SIAM J. Matrix Anal. Appl., 16, 172-191 (1995) · Zbl 0815.65050
[31] Gugercin, S.; Sorensen, D. C.; Antoulas, A. C., A modified low rank Smith method for large-scale Lyapunov equations, Numer. Algorithms, 32, 27-55 (2003) · Zbl 1034.93020
[32] Jessup, E. R.; Sorensen, D. C., A parallel algorithm for computing the singular value decomposition of a matrix, SIAM J. Matrix Anal. Appl., 15, 530-548 (1994) · Zbl 0797.65037
[33] Kellems, A.; Chaturantabut, S.; Sorensen, D. C.; Cox, S. J., Morphologically accurate reduced order modeling of spiking neurons, J. Comput. Neurosci., 28, 477-494 (2010)
[34] Lampe, J.; Rojas, M.; Sorensen, D. C.; Voss, H., Accelerating the LSTRS algorithm, SIAM J. Sci. Comput., 33, 175-194 (2011) · Zbl 1368.65096
[35] Lehoucq, R. B.; Sorensen, D. C., Deflation techniques for an implicitly restarted Arnoldi iteration, SIAM J. Matrix Anal. Appl., 17, 789-821 (1996) · Zbl 0863.65016
[36] Lehoucq, R. B.; Sorensen, D. C.; Yang, C., ARPACK Users’ Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods (1998), SIAM: SIAM Philadelphia · Zbl 0901.65021
[37] Li, J.-R.; White, J., Reduction of large circuit models via low rank approximate gramians, Int. J. Appl. Math. Comput. Sci., 11, 1151-1171 (2001) · Zbl 0995.93027
[38] Meerbergen, K.; Spence, A., Inverse iteration for purely imaginary eigenvalues with application to the detection of Hopf bifurcations in large-scale problems, SIAM J. Matrix Anal. Appl., 31, 1982-1999 (2010) · Zbl 1205.65156
[39] Moré, J. J.; Sorensen, D. C., Computing a trust region step, SIAM J. Sci. Statist. Comput., 4, 553-572 (1983) · Zbl 0551.65042
[40] Penzl, T., A cyclic low rank Smith method for large sparse Lyapunov equations, SIAM J. Sci. Comput., 21, 1401-1418 (2000) · Zbl 0958.65052
[41] Penzl, T., Algorithms for model reduction of large dynamical systems, Linear Algebra Appl., 415, 322-343 (2006), Reprint of Technical Report SFB393/99-40, TU Chemnitz, 1999 · Zbl 1092.65053
[42] Rojas, M.; Santos, A.; Sorensen, D. C., A new matrix-free algorithm for the large-scale trust-region subproblem, SIAM J. Optim., 11, 611-646 (2000) · Zbl 0994.65067
[43] Rojas, M.; Santos, A.; Sorensen, D. C., Algorithm 873: LSTRS: MATLAB software for large-scale trust- region subproblems and regularization, ACM Trans. Math. Software, 34 (2008), Article 11 · Zbl 1291.65177
[44] Rojas, M.; Sorensen, D. C., A trust-region approach to the regularization of large-scale discrete forms of ill-posed problems, SIAM J. Sci. Comput., 23, 1842-2860 (2002) · Zbl 1006.86004
[45] J. Rutter, A serial implementation of Cuppen’s divide and conquer algorithm for the symmetric eigenvalue problem, Tech. Rep. UCB/CSD 94/799, Domputer Science Division, University of California, Berkeley, 1994. LA- PACK Working Note 69.; J. Rutter, A serial implementation of Cuppen’s divide and conquer algorithm for the symmetric eigenvalue problem, Tech. Rep. UCB/CSD 94/799, Domputer Science Division, University of California, Berkeley, 1994. LA- PACK Working Note 69.
[46] Saad, Y., Variations on Arnoldi’s method for computing eigenelements of large unsymmetric matrices, Linear Algebra Appl., 34, 269-295 (1980) · Zbl 0456.65017
[47] Saad, Y., Chebyshev acceleration techniques for solving nonsymmetric eigen-value problems, Math. Comput., 42, 567-588 (1984) · Zbl 0539.65013
[48] Sorensen, D. C., Newton’s method with a model trust region modification, SIAM J. Numer. Anal., 19, 409-426 (1982) · Zbl 0483.65039
[49] Sorensen, D. C., Implicit application of polynomial filters in a k-step Arnoldi method, SIAM J. Matrix Anal. Appl., 13, 357-385 (1992) · Zbl 0763.65025
[50] Sorensen, D. C., Minimization of a large-scale quadratic function subject to a spherical constraint, SIAM J. Optim., 7, 141-162 (1997) · Zbl 0878.65044
[51] Sorensen, D. C., Numerical methods for large eigenvalue problems, Acta Numer., 11, 519-584 (2002) · Zbl 1105.65325
[52] Sorensen, D. C., Passivity preserving model reduction via interpolation of spectral zeros, Systems Control Lett., 54, 347-360 (2005) · Zbl 1129.93340
[53] Sorensen, D. C.; Tang, P. T.P., On the orthogonality of eigenvectors computed by divide-and-conquer techniques, SIAM J. Numer. Anal., 28, 1752-1775 (1991) · Zbl 0743.65039
[54] Sorensen, D. C.; Yang, C., A truncated RQ iteration for large scale eigenvalue calculations, SIAM J. Matrix Anal. Appl., 19, 1045-1073 (1998) · Zbl 0918.65023
[55] Wilkinson, J. H., The Algebraic Eigenvalue Problem (1965), Oxford University Press: Oxford University Press Oxford · Zbl 0258.65037
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.