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The Symmetric Eigenvalue Problem (Paperback, 2 Rev Ed)
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The Symmetric Eigenvalue Problem (Paperback, 2 Rev Ed)
Series: Classics in Applied Mathematics, No. 20
Expected to ship within 12 - 19 working days
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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, given
below, 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. Key Features:* Convergence theory for the Rayleigh
quotient iteration.* The direct rotation as a rival to Householder
reflectors.* 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
flavours of subspace iteration.
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