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1982•The Computer JournalOpen access

A Modified Bisection Algorithm for the Determination of the Eigenvalues of a Symmetric Quindiagonal Matrix

J. Shanehchi, David John Evans

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Abstract

In this note, we consider the implementation of the incomplete Sturm sequence evaluation,2 for the determination of the eigenvalues of a symmetric quindiagonal matrix A based on the bisection method. The application of the bisection method for quindiagonal matrices is described in Ref. 3 and therefore, we discuss the changes to the proposed method in order to improve efficiency when dealing with only a few of the lowest or highest eigenvalues of quindiagonal matrices.

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In this note, we consider the implementation of the incomplete Sturm sequence evaluation,2 for the determination of the eigenvalues of a symmetric quindiagonal matrix A based on the bisection method. The application of the bisection method for quindiagonal matrices is described in Ref. 3 and therefore, we discuss the changes to the proposed method in order to improve efficiency when dealing with only a few of the lowest or highest eigenvalues of quindiagonal matrices.

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Available abstract

In this note, we consider the implementation of the incomplete Sturm sequence evaluation,2 for the determination of the eigenvalues of a symmetric quindiagonal matrix A based on the bisection method. The application of the bisection method for quindiagonal matrices is described in Ref. 3 and therefore, we discuss the changes to the proposed method in order to improve efficiency when dealing with only a few of the lowest or highest eigenvalues of quindiagonal matrices.

Key concepts: Bisection method, Eigenvalues and eigenvectors, Bisection, Matrix (chemical analysis), Mathematics, Symmetric matrix, Algorithm, Order (exchange)

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