论文标题
四核矩阵和darboux转换的双子分组分解
Bidiagonal factorization of tetradiagonal matrices and Darboux transformations
论文作者
论文摘要
最近，提出了一个呈阳性双子分解的界限下赫森伯格矩阵的光谱定理。这些类型的矩阵是振荡的。在本文中，根据该双基因测定的双节分解，讨论了Lima-loureiro高几何多个正交多项式和Jacobi-Piñeiro多个正交多项式。研究了四核Hessenberg矩阵的DARBOUX转换，并给出了双子分解元素的基督佛尔公式，即，即以在起源处评估的递归多项式给出了bidiagonal分解。
Recently a spectral Favard theorem for bounded banded lower Hessenberg matrices that admit a positive bidiagonal factorization was presented. These type of matrices are oscillatory. In this paper the Lima-Loureiro hypergeometric multiple orthogonal polynomials and the Jacobi-Piñeiro multiple orthogonal polynomials are discussed at the light of this bidiagonal factorization for tetradiagonal matrices. The Darboux transformations of tetradiagonal Hessenberg matrices is studied and Christoffel formulas for the elements of the bidiagonal factorization are given, i.e., the bidiagonal factorization is given in terms of the recursion polynomials evaluated at the origin.
