论文标题
四核Hessenberg矩阵的阳性比二对角分解
Positive bidiagonal factorization of tetradiagonal Hessenberg matrices
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。在本文的情况下，就持续的分数而言，对于振荡性四核分子赫森伯格基质的振荡性均具有阳性的双对角分解。振荡性四核toeplitz矩阵被视为接受双节性分解阳性的基质的案例研究。此外，事实证明，振荡性带状的黑森贝格矩阵是在射线中组织的，射线的起源没有阳性的双节性分解，并且射线的所有内部点具有如此阳性的双节性分解。
Recently a spectral Favard theorem for bounded banded lower Hessenberg matrices that admit a positive bidiagonal factorization was presented. In this paper conditions, in terms of continued fractions, for an oscillatory tetradiagonal Hessenberg matrix to have such positive bidiagonal factorization are found. Oscillatory tetradiagonal Toeplitz matrices are taken as a case study of matrix that admits a positive bidiagonal factorization. Moreover, it is proved that oscillatory banded Hessenberg matrices are organized in rays, with the origin of the ray not having the positive bidiagonal factorization and all the interior points of the ray having such positive bidiagonal factorization.
