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Laguerre's iteration and the method of traces for eigenproblems

✍ Scribed by Christopher T. Lenard

Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
148 KB
Volume
3
Category
Article
ISSN
0893-9659

No coin nor oath required. For personal study only.

✦ Synopsis

In this note we show that Laguerre's method for finding the root of a polynomial when applied to the charecteristic polynomial of a matrix is the same as the method of traces for determining an eigenpair of that matrix.

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Solitary waves, cnoidal waves, and shock waves can be computed by solving a nonlinear eigenvalue problem, which in discretized form is a system of nonlinear algebraic equations. Unfortunately, many such systems are singular because the solution is not unique until one or more additional constraints