SIAM Homepage | Search Catalog | New Books | Author Index | Series Index | Title Index | View My Shopping Cart

The catalog and shopping cart are hosted for SIAM by EasyCart. Your transaction is secure. If you have any questions about your order, contact

Purchase Now!

The Symmetric Eigenvalue ProblemThe Symmetric Eigenvalue Problem

Beresford N. Parlett

Classics in Applied Mathematics 20

According to Parlett, "Vibrations are everywhere, and so too are the eigenvalues associated with them. As mathematical models invade more and more disciplines, we can anticipate a demand for eigenvalue calculations in an ever richer variety of contexts." Anyone who performs these calculations will welcome the reprinting of Parlett's book (originally published in 1980).

In this unabridged, amended version, Parlett covers aspects of the problem that are not easily found elsewhere. The chapter titles convey the scope of the material succinctly. The aim of the book is to present mathematical knowledge that is needed in order to understand the art of computing eigenvalues of real symmetric matrices, either all of them or only a few. The author explains why the selected information really matters and he is not shy about making judgments. The commentary is lively but the proofs are terse.

The first nine chapters are based on a matrix on which it is possible to make similarity transformations explicitly. The only source of error is inexact arithmetic. The last five chapters turn to large sparse matrices and the task of making approximations and judging them.


  • Convergence theory for the Rayleigh quotient iteration
  • Eigenvectors of tridiagonals
  • Convergence theory, simpler than Wilkinson's, for Wilkinson's shift strategy in QL and QR
  • New proofs and sharper results for error bounds
  • Optimal properties of Rayleigh-Ritz approximations
  • Approximation theory from Krylov subspaces, Paige's theorem for noisy Lanczos algorithms, and semiorthogonality among Lanczos vectors
  • Four flavors of subspace iteration

1998 / xxiv + 398 pages / Softcover / ISBN-13: 978-0-898714-02-9 / ISBN-10: 0-89871-402-8 /
List Price $83.50 / Member Price $58.45 / Order Code CL20
Quantity desired

Search our catalog for:

Shopping cart provided by:
Select quantity and list or member price and then click the "Click to Order" button to add books to your shopping cart.
Banner art adapted from a figure by Hinke M. Osinga and Bernd Krauskopf (University of Auckland, NZ.)