Acta Applicandae Mathematica

, Volume 21, Issue 3, pp 291–313

Error-free matrix symmetrizers and equivalent symmetric matrices

  • V. Ch. Venkaiah
  • S. K. Sen

DOI: 10.1007/BF00047212

Cite this article as:
Venkaiah, V.C. & Sen, S.K. Acta Appl Math (1990) 21: 291. doi:10.1007/BF00047212


A symmetrizer of the matrix A is a symmetric solution X that satisfies the matrix equation XA=A′X. An exact matrix symmetrizer is computed by obtaining a general algorithm and superimposing a modified multiple modulus residue arithmetic on this algorithm. A procedure based on computing a symmetrizer to obtain a symmetric matrix, called here an equivalent symmetric matrix, whose eigenvalues are the same as those of a given real nonsymmetric matrix is presented.

AMS subject classifications (1980)

65F 65G 

Key words

Complex symmetric matrix equivalent symmetric matrices error-free matrix symmetrizers floating-point modular arithmetic Hessenberg matrices nonsymmetric eigenvalue problem parallel implementation QR transformation 

Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • V. Ch. Venkaiah
    • 1
  • S. K. Sen
    • 1
  1. 1.Department of Applied MathematicsIndian Institute of ScienceBangaloreIndia

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