# 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)
An iterative method for symmetric solutions and optimal approximation solution of the system of matrix equations ${A}_{1}X{B}_{1}={C}_{1},{A}_{2}X{B}_{2}={C}_{2}$. (English) Zbl 1134.65032

The symmetric solutions of the systems of matrix equations ${A}_{1}X{B}_{1}={C}_{1}$, ${A}_{2}X{B}_{2}={C}_{2}$ can not be easily obtained by applying matrix decompositions. The authors are proposing an iterative method to solve systems of matrix equations, where when the system of matrix equations is consistent, and its solution can be obtained within finite iterative steps, and its least-norm solution can be obtained by choosing a special kind of initial iterative matrix. Additionally, its optimal approximation solution to a given matrix can be derived by finding the least-norm symmetric solution of a new system of matrix equations ${A}_{1}\stackrel{^}{X}{B}_{1}={\stackrel{^}{C}}_{1}$, ${A}_{2}\stackrel{^}{X}{B}_{2}={\stackrel{^}{C}}_{2}$.

Finally, the author demonstrates the applicability of the proposed method on systems of matrix equations.

##### MSC:
 65F30 Other matrix algorithms 15A24 Matrix equations and identities 65F10 Iterative methods for linear systems