zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
A completed theory of the unsymmetric Lanczos process and related algorithms. I. (English) Zbl 0760.65039
This substantial paper provides a general theory of the unsymmetric Lanczos algorithm. The whole theory is here developed from the point of view of orthogonal polynomials and Padé approximants. A rather comprehensive introduction to this subject is therefore provided. The recurrence relations for formal orthogonal polynomials are then interpreted in a matrix setting, leading naturally to the Lanczos process. Using the connection to Padé approximants, the block structure theorem for those is used to overcome the difficulties associated with nongeneric break-down. Connections are also established to other algorithms from the same group as Lanczos’s, such as BIORES or BIORTHORES, and bi-conjugate gradients.

65F15Eigenvalues, eigenvectors (numerical linear algebra)
65F10Iterative methods for linear systems
41A21Padé approximation
Full Text: DOI