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 approximations with sparse factors. I: Basic algorithms and error analysis. (English) Zbl 1003.65041
The problem of computing low-rank approximations of matrices is cast in the framework of an optimization problem. The low-rank approximations are written in a factorized form with sparse factors and the degree of sparsity of the factors is traded off for reduced reconstruction error by certain user defined parameters. Algorithms and heuristics for finding approximate solutions to this optimization problem are proposed. A detailed error analysis of the proposed algorithms is given and a comparison of the computed sparse low rank approximations with those obtained from singular value decomposition (SVD) is done. Specifically, the authors prove that the reconstruction errors of the computed sparse low-rank approximations are within a constant factor of those that are obtained by SVD. Several numerical experiments are conducted to illustrate the various numerical and efficiency issues of the proposed algorithms. Some directions for future research are pointed out.

MSC:
65F30Other matrix algorithms
65F20Overdetermined systems, pseudoinverses (numerical linear algebra)
WorldCat.org
Full Text: DOI