Computational Methods for Linear Matrix Equations

2016/01/01 by V. Simoncini, Valeria Simoncini · 27 citations
Computer Science · Mathematics · Physics and Astronomy · #Matrix Theory and Algorithms #Numerical methods for differential equations #Electromagnetic Scattering and Analysis

paper · doi:10.1137/130912839

Abstract

Given the square matrices A, B, D, E and the matrix C of conforming dimensions, we consider the linear matrix equation AXE + DXB = C in the unknown matrix X. Our aim is to provide an overview of the major algorithmic developments that have taken place over the past few decades in the numerical solution of this and related problems, which are producing reliable numerical tools in the formulation and solution of advanced mathematical models in engineering and scientific computing.

Citations

• The general problem of the stability of motion
• TT-cross approximation for multidimensional arrays
• Tensor Decompositions and Applications
• Rational Krylov sequence methods for eigenvalue computation
• The Sylvester equation and approximate balanced reduction
• Principal component analysis in linear systems: Controllability, observability, and model reduction
• Toward solution of matrix equation X = Af ( X ) B + C

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Related

• Numerical solution of a class of quasi-linear matrix equations
• On the solution of the linear matrix equation X=Af(X)B+C
• Numerical Linear Algebra: Least Squares, QR and SVD
• Kaczmarz-Type Method for Solving Matrix Equation AXB=C
• Matrix Decomposition and Applications