Numerical Techniques for Solving the Matrix Equation X = AX^TB + C

Numerical Techniques for Solving the Matrix Equation X = AX^TB + C

謝志達(Chih-Da Shieh)

指導教授 ： 林敏雄

國立中正大學/理學院/數學系研究所/碩士(2013年)

摘要

無資料

關鍵字

矩陣方程 ； 史密斯疊代 ； 共扼梯度 ； 數值結果

並列摘要

We do some numerical results to verify the theory. In fact, we use several methods, such as Conjugate Gradient method(CG), Smith Iterative method and Structure-preserving Doubling Algorithm(SDA). These methods are well known and have been applied in many different fields. So we are very curious about the pros and cons of these methods on solving the equation X = AX^TB+C. In order to compare these methods are good or bad, we create some tables to demonstrate numerical experiments. The accuracy of these methods, the number of iterations and the CPU time are expressed in our tables.

並列關鍵字

Numerical solution ； Matrix equation ； Structure-preserving doubling algorithm ； Smith iteration ； Conjugate gradient ； T-Stein equation

參考文獻

equation AX ± X⋆B⋆ = C. Appl. Math. Comput., 218(17):8393–8407, 2012.

algorithm for nonsymmetric algebraic Riccati equation. Numer. Math., 103(3):393–

[3] Tongsong Jiang and MushengWei. On solutions of the matrix equations X−AXB =

C and X − AXB = C. Linear Algebra Appl., 367:225–233, 2003.

with the minimum-norm to general matrix equations via iteration. Appl. Math.