| Autor: |
RINGH, EMIL, JARLEBRING, ELIAS |
| Předmět: |
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| Zdroj: |
SIAM Journal on Matrix Analysis & Applications; 2021, Vol. 42 Issue 2, p775-799, 25p |
| Abstrakt: |
We investigate a technique to transform a linear two-parameter eigenvalue problem into a nonlinear eigenvalue problem (NEP). The transformation stems from an elimination of one of the equations in the two-parameter eigenvalue problem, by considering it as a (standard) generalized eigenvalue problem. We characterize the equivalence between the original and the nonlinearized problem theoretically and show how to use the transformation computationally. Special cases of the transformation can be interpreted as a reversed companion linearization for polynomial eigen value problems, as well as a reversed (less known) linearization technique for certain algebraic eigen valueproblems with square-root terms. Moreover, by exploiting the structure of the NEP we present algo-rithm specializations for NEP methods, although the technique also allows general solution methods for NEPs to be directly applied. The nonlinearization is illustrated in examples and simulations,with focus on problems where the eliminated equation is of much smaller size than the other two-parameter eigenvalue equation. This situation arises naturally in domain decomposition techniques.A general error analysis is also carried out under the assumption that a backward stable eigensolveris used to solve the eliminated problem, leading to the conclusion that the error is benign in this situation [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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