A New Algorithm for the Symmetric Tridiagonal Eigenvalue Problem
Victor Y. Pan,James Demmel +1 more
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TL;DR: A novel approach to approximate within ϵ to all the eigenvalues of an n × n symmetric tridiagonal matrix A using at most n2 arithmetic operations where λ1 and λn denote the extremal eigen values of A.
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About: This article is published in Journal of Complexity. The article was published on 01 Sep 1993. and is currently open access. The article focuses on the topics: Tridiagonal matrix & Tridiagonal matrix algorithm.
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Complexity of computations with matrices and polynomials
TL;DR: The complexity of polynomial and matrix computations, as well as their various correlations to each other and some major techniques for the design of algebraic and numerical algorithms are reviewed.
Bisection acceleration for the symmetric tridiagonal eigenvalue problem
Victor Y. Pan,Elliot Linzer +1 more
TL;DR: New algorithms that accelerate the bisection method for the symmetric tridiagonal eigenvalue problem by using a new variant of Newton's iteration that reaches cubic convergence to the well separated eigenvalues.
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Solving a Polynomial Equation: Some History and Recent Progress
TL;DR: The history of the algorithmic approach to this problem is recalled, some successful solution algorithms are reviewed, and some algorithms of 1995 are outlined that solve this problem at a surprisingly low computational cost.