zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Matrix algorithms. Vol. 2: Eigensystems. (English) Zbl 0984.65031
Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics). xix, 469 p. (2001).

This second volume in a series of 5 on matrix algorithms is devoted to eigenvalue-eigenvector computations. As in the first volume on basic decompositions (1998; Zbl 0910.65012), the approach is very constructive, algorithmic, and self contained. The author has chosen not to heavily cross reference between the different volumes but to assume a general understanding of what is needed from the previous theory and algorithms. The first part concentrates on general dense matrices and the main issues are subsequently: the general theory, the QR algorithm, and the symmetric eigenvalue problem. Also singular values and the generalized eigenvalue problem are discussed here. In the second part large matrices are treated. Again the general theory is given and is followed by Krylov methods (in particular Arnoldi and Lanczos). The last chapter shifts to subspace iteration and the Jacobi-Davidson method.

The material for this second volume is less elementary than in the first volume. Yet the author succeeds again in picking up the essential stepping stones to allow the student or the practinoner, who might not be a specialist in numerical linear algebra, to safely embark the reading of this volume. It confirms the expectation that the whole series will grow out to be a reference work for the next generation.

MSC:
65F15Eigenvalues, eigenvectors (numerical linear algebra)
65-01Textbooks (numerical analysis)
00A06Mathematics for non-mathematicians
65F20Overdetermined systems, pseudoinverses (numerical linear algebra)