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)
Conjugate gradient methods for Toeplitz systems. (English) Zbl 0863.65013
The use of preconditioned conjugate gradient methods to solve linear systems of equations with Toeplitz matrices is discussed. Using this iterative method, the complexity is reduced from O(nlog 2 n) operations for fast direct Toeplitz solvers to O(nlogn). The authors review the use of preconditioners based on circulant matrices, embedding, minimization of norms, optimal transform (like the fast Fourier or sine transform) and band Toeplitz matrices. The various techniques are applied for solving partial differential equations, queuing problems, signal and image restoration, integral equations and time series analysis (filtering).
65F10Iterative methods for linear systems
68U10Image processing (computing aspects)
65F35Matrix norms, conditioning, scaling (numerical linear algebra)
65R20Integral equations (numerical methods)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65C99Probabilistic methods, simulation and stochastic differential equations (numerical analysis)