Continuation of eigendecompositions

Future Generation Computer Systems - Tập 19 - Trang 1125-1137 - 2003
L. Dieci1, A. Papini2
1School of Mathematics, Georgia Tech, Atlanta, GA 30332, USA
2Dipartimento di Energetica, Univ. of Florence, 50134 Florence, Italy

Tài liệu tham khảo

E. Allgower, K. Georg, Continuation and path following, Acta Numer. (1993) 1–64. M. Baumann, U. Helmke, Diagonalization of time varying symmetric matrices, University of Wurzburg, Preprint, 2002. Bavely, 1979, An algorithm for computing reducing subspaces by block-diagonalization, SIAM J. Numer. Anal., 16, 359, 10.1137/0716028 Beyn, 1990, The numerical computation of connecting orbits in dynamical systems, IMA J. Numer. Anal., 10, 379, 10.1093/imanum/10.3.379 Bunse-Gerstner, 1991, Numerical computation of an analytic singular value decomposition by a matrix valued function, Numer. Math., 60, 1, 10.1007/BF01385712 Demmel, 1987, Three methods for refining estimates of invariant subspaces, Computing, 38, 43, 10.1007/BF02253743 Demmel, 2001, An efficient algorithm for locating and continuing connecting orbits, SIAM J. Sci. Comput., 22, 81, 10.1137/S1064827598344868 Dieci, 1999, On smooth decomposition of matrices, SIAM J. Matrix Anal. Appl., 20, 800, 10.1137/S0895479897330182 Dieci, 2001, Continuation of invariant subspaces, Appl. Numer. Lin. Algebra, 8, 317, 10.1002/nla.245 Friedman, 2001, An improved detection of bifurcations in large nonlinear systems via the continuation of invariant subspaces algorithm, Int. J. Bifurcat. Chaos, 11, 2277, 10.1142/S0218127401003255 Gingold, 1992, Globally analytic triangularization of a matrix function, Lin. Algebra Appl., 169, 75, 10.1016/0024-3795(92)90172-7 Golub, 1979, A Hessenberg–Schur method for the problem AX+XB=C, IEEE Trans. Automat. Contr., 24, 909, 10.1109/TAC.1979.1102170 G.H. Golub, C.F. Van Loan, Matrix Computations, 2nd ed., Johns Hopkins University Press, Baltimore, MD, 1989. B. Kagström, Computation of matrix functions. Technical Report, Report UMINF-58.77, Dept. Inf. Processing, University of Umea, Umea, Sweden, 1977. T. Kato, Perturbation Theory for Linear Operators, 2nd ed., Springer, Berlin, 1976. H. Keller, Numerical Methods in Bifurcation Problems, Tata Institute of Fundamental Research, Springer, Bombay, 1987. Mehrmann, 1992, Numerical methods for the computation of analytic singular value decompositions, Electr. Trans. Numer. Anal., 1, 72 Rheinboldt, 1988, On the computation of multi-dimensional solution manifolds of parametrized equations, Numer. Math., 53, 165, 10.1007/BF01395883 Wright, 1992, Differential equations for the analytical singular value decomposition of a matrix, Numer. Math., 63, 283, 10.1007/BF01385862