Extending LSQR methods to solve the generalized Sylvester‐transpose and periodic Sylvester matrix equations
Masoud Hajarian · Mathematical Methods in the Applied Sciences · 2013
It is well known that the least‐squares QR‐factorization (LSQR) algorithm is a powerful method for solving linear systems Ax = b and unconstrained least‐squares problem minx | | Ax − b | | . In the paper, the LSQR approach is developed to obtain iterative algorithms for solving the generalized Sylvester‐transpose matrix equation urn:x-wiley:01704214:media:mma2955:mma2955-math-0001 the minimum Frobenius norm residual problem urn:x-wiley:01704214:media:mma2955:mma2955-math-0002 and the periodic Sylvester matrix equation urn:x-wiley:01704214:media:mma2955:mma2955-math-0003 Numerical results are given to illustrate the effect of the proposed algorithms. Copyright © 2013 John Wiley & Sons, Ltd.