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Two Parameter Iteration Methods for Coupled Sylvester Matrix Equations

East Asian Journal on Applied Mathematics, 2018
We consider two parameter iteration methods for the coupled Sylvester matrix equations AX + Y B = E CX + Y D = F. Having established the convergence of the algorithms, we discuss the choice of optimal parameters. Numerical examples show the efficiency of
Chuang Ma
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A simple matrix alteration method

Applied Mathematical Sciences, 2019
We use a well known formula given by C.G. Broyden for the solution of an equation system in a slightly different manner. We alter the given matrix J of a given linear matrix equation y0 = Jx0 into a matrix H of same size such that for fixed x0 we receive
T. Wieder
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Recurrences for Entries of Powers of Matrices

The Fibonacci quarterly, 2017
In this note, giving course to a challenge in a recent paper of Larcombe [2], we find the entries of any nth power of a 3×3 matrix, and as a byproduct, we recover Larcombe’s result on 2× 2 matrices.
Gabriela Stanica, P. Stănică
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How and Why to Solve the Operator Equation AX−XB = Y

, 1997
R. Bhatia, P. Rosenthal
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The Alternating Direction Methods for Solving the Sylvester-Type Matrix Equation AXb + CX^⊤D = E*

, 2017
Yifen Ke, Changfeng Ma
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The Jacobsthal and Jacobsthal-Lucas numbers via square roots of matrices

, 2016
Saadet Arslan, Fikri Köken
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k-Jacobsthal and k-Jacobsthal Lucas Matrix Sequences

, 2016
S. Uygun, H. Eldogan
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Convergence rates of a class of predictor-corrector iterations for the nonsymmetric algebraic Riccati equation arising in transport theory