首页|On the non-symmetric semidefinite Procrustes problem
On the non-symmetric semidefinite Procrustes problem
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NSTL
Elsevier
In this paper, we consider the non-symmetric positive semidefinite Procrustes (NSPSDP) problem: Given two matrices X, B is an element of R-n,R-m , find the matrix A is an element of R-n,R-n that minimizes the Frobenius norm of AX - B and which is such that A + A(T) is positive semidefinite. We generalize the semi-analytical approach for the symmetric positive semidefinite Procrustes problem, where A is required to be positive semidefinite, that was proposed by Gillis and Sharma (A semi-analytical approach for the positive semidefinite Procrustes problem, Linear Algebra Appl. 540, 112-137, 2018). As for the symmetric case, we first show that the NSPSDP problem can be reduced to a smaller NSPSDP problem that always has a unique solution and where the matrix X is diagonal and has full rank. Then, an efficient semi-analytical algorithm to solve the NSPSDP problem is proposed, solving the smaller and well-posed problem with a fast gradient method which guarantees a linear rate of convergence. This algorithm is also applicable to solve the complex NSPSDP problem, where & nbsp;& nbsp;X,B is an element of C-n,C-m, as we show that the complex NSPSDP problem can be written as an overparametrized real NSPSDP problem. The efficiency of the proposed algorithm is illustrated on several numerical examples. (C) 2022 Elsevier Inc. All rights reserved.
NSTL
Elsevier
