# Computing the Minimum Eigenvalue of a Symmetric Positive Definite Toeplitz Matrix with Spectral Transformation Lanczos Methods

• Thomas Huckle
Part of the International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique book series (ISNM, volume 96)

## Abstract

A matrix T is Toeplitz if the elements on each diagonal are all equal. Thus, for the real symmetric case T is of the form
$$T = T({{t}_{0}},{{t}_{1}}, \ldots ,{{t}_{{n - 1}}}): = \left( {\begin{array}{*{20}{c}} {{{t}_{0}}} & {{{t}_{1}}} & \cdots & \cdots & {{{t}_{{n - 1}}}} \\ {{{t}_{1}}} & {{{t}_{0}}} & {{{t}_{1}}} & {} & \vdots \\ \vdots & {{{t}_{1}}} & \ddots & \ddots & \vdots \\ \vdots & {} & \ddots & \ddots & {{{t}_{1}}} \\ {{{t}_{{n - 1}}}} & \cdots & \cdots & {{{t}_{1}}} & {{{t}_{0}}} \\ \end{array} } \right).$$

## Keywords

Toeplitz Matrix Minimum Eigenvalue Toeplitz Matrice Lanczos Method Circulant Matrice
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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