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01546539
j
01546539
Golub, Gene H.
van der Vorst, Henk A.
Eigenvalue computation in the 20th century.
J. Comput. Appl. Math. 123, No.1-2, 35-65 (2000).
2000
Elsevier Science B.V. (North-Holland), Amsterdam
EN
Lanczos method
historical survey
canonical forms
reduction algorithms
eigenvalue problems
Jacobi method
power method
iteration methods
singular value decomposition
nonlinear eigenvalue problems
pseudospectra
homotopy methods
doi:10.1016/S0377-0427(00)00413-1
This excellent paper gives a comprehensive survey of the computational methods for eigenvalue problems. Canonical forms, perturbation theorems are first introduced, and then the Jacobi method and the power method are discussed. Reduction algorithms and iteration methods are the subjects of the next part. Among related topics the singular value decomposition, nonlinear eigenvalue problems, pseudospectra, and homotopy methods are analyzed. A brief summary of related software concludes the paper.
F.Szidarovszky (Tucson)