Pad¨¦ Approximant Method Of Computing The Matrix Sign Function And Invariant Subspaces

This paper deals with one typical problem of matrix eigenvalue: the problem of invariant subspace. When using many classical algorithm which settle with matrix eigenvalue problem to deal with this problem,there is so much dif-ficulty,unfeasible sometimes. The problem of invariant subspace catches many academician's eyes recent years, and matrix sign function technique is been produced.In this paper, we firstly show the definition and character of matrix sign function, review the classical algorithm which compute matrix sign function, then analyze some improved algorithm in history. We show the rational iterative algorithm and low Pade iterative algorithm, give detailed analysis of this tow algorithms'astringency. At the same time, we primarily discuss use high order Pade approach which need lower account to compute proximate invariant subspace. Finally, numerical example of this paper show that this two algorithms are resultful for computing invariant subspaces.This paper has two most contributions:1. We firstly bring forward that using one order Pade iterative algorithm to compute matrix sign function, then analyze and proof that this algorithm his three order convergence rate. Succeed using this algorithm to compute invariant subspaces which have some characters.2. Bring forward one rational transformation of matrix sign function. When matrix is in Hermite case, this algorithm can use QR decompose to avoid computing invert.