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)
SLEPc: a scalable and flexible toolkit for the solution of eigenvalue problems. (English) Zbl 1136.65315
Summary: The Scalable Library for Eigenvalue Problem Computations (SLEPc) is a software library for computing a few eigenvalues and associated eigenvectors of a large sparse matrix or matrix pencil. It has been developed on top of PETSc and enforces the same programming paradigm.The emphasis of the software is on methods and techniques appropriate for problems in which the associated matrices are sparse, for example, those arising after the discretization of partial differential equations. Therefore, most of the methods offered by the library are projection methods such as Arnoldi or Lanczos, or other methods with similar properties. SLEPc provides basic methods as well as more sophisticated algorithms. It also provides built-in support for spectral transformations such as the shift-and-invert technique. SLEPc is a general library in the sense that it covers standard and generalized eigenvalue problems, both Hermitian and non-Hermitian, with either real or complex arithmetic. SLEPc can be easily applied to real world problems. To illustrate this, several case studies arising from real applications are presented and solved with SLEPc with little programming effort. The addressed problems include a matrix-free standard problem, a complex generalized problem, and a singular value decomposition. The implemented codes exhibit good properties regarding flexibility as well as parallel performance.
MSC:
65F15Eigenvalues, eigenvectors (numerical linear algebra)
65F50Sparse matrices (numerical linear algebra)
65Y15Packaged methods in numerical analysis
Software:
JDQR; SLEPc; TRLan; JDQZ; PETSc