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)
Low-rank matrix approximation using the Lanczos bidiagonalization process with applications. (English) Zbl 0962.65038
Approximations B (of rank j) of a given large non-square matrix A are studied. Their optimal form is defined as a minimizer of the Frobenius norm of the difference A-B. In principle, it can be constructed via a j-dimensional part (projection) of a certain diagonalized form of A. In such a setting one would need the full singular value decomposition of A (which generalizes the current diagonalization using two orthogonal matrices P and Q). The paper offers a cheaper algorithm based on the Lanczos bidiagonalization. The authors perform the error and stopping analysis and demonstrate that a mere one-sided re-orthogonalization of this process guarantees a sufficient precision. A collection of matrices from several application areas is used in illustrative tests.

MSC:
65F20Overdetermined systems, pseudoinverses (numerical linear algebra)
65F50Sparse matrices (numerical linear algebra)