A New O(n) Algorithm for the Symmetric Tridiagonal Eigenvalue/Eigenvector Problem by Inderjit Singh Dhillon Doctor of Philosophy in Computer Science University of California, Berkeley Professor James W. Demmel, Chair Computing the eigenvalues and orthogonal eigenvectors of an n n symmetric tridiagonal matrix is an important task that arises while solving any symmetric eigenproblem. All practica...

A Jacobi matrix with matrix entries is a self-adjoint block tridiagonal matrix with invertible blocks on the off-diagonals. The Weyl surface describing the dependence of Green’s matrix on the boundary conditions is interpreted as the set of maximally isotropic subspace of a quadratic from given by the Wronskian. Analysis of the possibly degenerate limit quadratic form leads to the limit point/l...

In this paper, we consider an approach based on the elementary matrix theory. other words, take into account generalized Gaussian Fibonacci numbers. context, a general tridiagonal family. Then, obtain determinants of family via Chebyshev polynomials. Moreover, one type matrix, whose are Horadam hybrid polynomials, i.e., most form its by means polynomials second kind. We provided several illustr...

Tridiagonal matrix inversion is an important operation with many applications. It arises frequently in solving discretized one-dimensional elliptic partial differential equations, and forms the basis for algorithms block tridiagonal PDEs higher-dimensions. In such systems, this often scaling bottleneck parallel computation. paper, we derive a hybrid multigrid-Thomas algorithm designed to effici...

We propose two ways for determining the Green's matrix for problems admitting Hamiltonians that have infinite symmetric tridiagonal (i.e. Jacobi) matrix form on some basis representation. In addition to the recurrence relation comming from the Jacobi-matrix, the first approach also requires the matrix elements of the Green's operator between the first elements of the basis. In the second approa...

The purpose of this paper is the construction of invariant regions in which we establish the global existence of solutions for reaction-diffusion systems (three equations) with a tridiagonal matrix of diffusion coefficients and with nonhomogeneous boundary conditions after the work of Kouachi (2004) on the system of reaction diffusion with a full 2-square matrix. Our techniques are based on inv...

In this report a way to apply high level Blas to the tridiagonalization process of a symmetric matrix A is investigated. Tridiagonalization is a very important and work-intensive preprocessing step in eigenvalue computations. It also arises as a very central part of the material sciences code Wien 97 (Blaha et al. [12]). After illustrating the drawbacks and limitations of the tridiagonalization...

A selfadjoined block tridiagonal matrix with positive definite blocks on the off-diagonals is by definition a Jacobi matrix with matrix entries. Transfer matrix techniques are extended in order to develop a rotation number calculation for its eigenvalues. This is a matricial generalization of the oscillation theorem for the discrete analogues of Sturm-Liouville operators. The three universality...

Given a univariate complex polynomial f(x) of degree n with rational coe cients expressed as a ratio of two integers < 2, the root problem is to nd all the roots of f(x) up to speci ed precision 2 . In this paper we assume the arithmetic model for computation. We give an improved algorithm for nding a well-isolated splitting interval and for fast root proximity veri cation. Using these results,...