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Accelerated bisection techniques for tri- and quindiagonal matrices

✍ Scribed by Graham Baker

Book ID
102960402
Publisher
John Wiley and Sons
Year
1992
Tongue
English
Weight
717 KB
Volume
35
Category
Article
ISSN
0029-5981

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✦ Synopsis

This paper considers accelerated bisection methods for calculating the eigenvalues of symmetric tridiagonal and quindiagonal matrices using cubic polynomial interpolation, as well as first and second order Newton iteration. Recursive relations based on the Sturm sequences are presented for the Newton type methods. The relations use a convenient scaling which retains the relative magnitudes in the iterative schemes but which avoids numerical overflow. Numerical examples show a significant increase in convergence rate.

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In this paper we discuss, study and compare two linear algorithms for the triangulation reΓΏnement problem: the known longest-side (triangle bisection) reΓΏnement algorithm, as well as a new algorithm that uses longest side bisection techniques for reΓΏning Delaunay triangulations. We show that the aut