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)
Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle. (English) Zbl 1143.65035
By extending the well-known Jacobi and Gauss-Seidel iterations for 𝐀𝐱=𝐛, the iterative solutions of matrix equations 𝐀𝐗𝐁=𝐅 and generalized Sylvester matrix equations 𝐀𝐗𝐁+𝐗𝐁=𝐅 (including the Sylvester equation 𝐀𝐗+𝐗𝐁=𝐅 as a special case) are studied, and a gradient based and a least-squares based iterative algorithms for the solution is proved. It is proved that the iterative solution always converges to the exact solution for any initial values. The basic idea is to regard the unknown matrix 𝐗 to be solved as the parameters of a system to be identified, and to obtain the iterative solutions by applying the hierarchical identification principle. Finally, the algorithms are tested and their effectiveness is shown using a numerical example.
65F30Other matrix algorithms