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Numerical Solution of a Semilinear Matrix Equation of the Stein Type in the Normal Case

Numerical Solution of a Semilinear Matrix Equation of the Stein Type in the Normal Case It is known that the solution of the semilinear matrix equation X − AX*B = C can be reduced to solving the classical Stein equation. The normal case means that the coefficients on the left-hand side of the resulting equation are normal matrices. A technique for solving the original semilinear equation in the normal case is proposed. For equations of the order n = 3000, this allows us to cut the time of computation almost in half, compared toMatlab’s library function dlyap, which solves Stein equations in the Matlab package. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Moscow University Computational Mathematics and Cybernetics Springer Journals

Numerical Solution of a Semilinear Matrix Equation of the Stein Type in the Normal Case

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Allerton Press, Inc.
Subject
Mathematics; Mathematics, general
ISSN
0278-6419
eISSN
1934-8428
DOI
10.3103/S0278641918020036
Publisher site
See Article on Publisher Site

Abstract

It is known that the solution of the semilinear matrix equation X − AX*B = C can be reduced to solving the classical Stein equation. The normal case means that the coefficients on the left-hand side of the resulting equation are normal matrices. A technique for solving the original semilinear equation in the normal case is proposed. For equations of the order n = 3000, this allows us to cut the time of computation almost in half, compared toMatlab’s library function dlyap, which solves Stein equations in the Matlab package.

Journal

Moscow University Computational Mathematics and Cybernetics – Springer Journals

Published: May 30, 2018

References

  • Toward solution of matrix equation X = Af(X)B + C
    Zhou, B.; Lam, J.; Duan, G.-R.
  • Numerical Solution ofMatrix Equations
    Ikramov, Kh. D.
  • Matrix Computations
    Golub, G. H.; Loan, Ch.