Detecting a hyperbolic quadratic eigenvalue problem by using a subspace algorithm

Pandur, Marija Miloloža

doi:10.1007/s11075-019-00702-0

Cited by 1 publication

(4 citation statements)

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“…In the following experiment, we apply Algorithm 3.2 to the matrix pair (A, B) from (20). We emphasize that there exist algorithms for detecting a hyperbolic QEP that work directly with matrices M , D, and K, which reduces storage requirements and the cost per iteration, such as [3,52,54]. We recommend [52, preconditioned variant of Algorithm 2] for large quadratics 9 .…”

Section: Matrix Pairs Obtained By Linearization Of the Quadratic Eige...mentioning

confidence: 99%

“…We construct a set of 40 overdamped quadratics of order n = 500 with the following eigenvalue distribution, as in [52]:…”

Section: Matrix Pairs Obtained By Linearization Of the Quadratic Eige...mentioning

confidence: 99%

“…Text copied from[52, Introduction] 9. The subspace Algorithm 3.1 for detecting positive definite matrix pairs is analogous to [52, Algorithm 1] for detecting hyperbolic quadratic eigenvalue problems.…”

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confidence: 99%

“…The subspace Algorithm 3.1 for detecting positive definite matrix pairs is analogous to [52, Algorithm 1] for detecting hyperbolic quadratic eigenvalue problems. Also see the discussion in [52, Section 3.1] and the experiments in[52, Section 4.2].…”

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confidence: 99%

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Subspace algorithms for detecting a definite Hermitian matrix pair

Pandur

2023

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The Hermitian pair (A,B) is called definite if some real linear combination of the matrices A and B is a positive definite matrix. There are several reasons why it is important to detect whether a given matrix pair is definite. Determining whether a given matrix pair is definite is not straightforward. There exist different kinds of algorithms for that task. Most of them are not appropriate for medium-size or large-size matrix pairs. We propose subspace algorithms for medium-size or large-size matrix pairs that are based on iterative testing of small compressed Hermitian matrix pairs formed by using subspaces of small dimensions. First, we propose a new basic subspace algorithm for detecting definite matrix pairs. Furthermore, we propose a specialized algorithm and its preconditioned variant. In this preconditioned variant, we need to solve several systems of linear equations. These systems can be solved only approximately and not necessarily in every iteration step. Numerical experiments demonstrate the efficiency of our specialized algorithm.

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Section: Matrix Pairs Obtained By Linearization Of the Quadratic Eige...mentioning

confidence: 99%

“…We construct a set of 40 overdamped quadratics of order n = 500 with the following eigenvalue distribution, as in [52]:…”

Section: Matrix Pairs Obtained By Linearization Of the Quadratic Eige...mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Subspace algorithms for detecting a definite Hermitian matrix pair

Pandur

2023

Preprint

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show abstract

Detecting a hyperbolic quadratic eigenvalue problem by using a subspace algorithm

Cited by 1 publication

References 16 publications

Subspace algorithms for detecting a definite Hermitian matrix pair

Subspace algorithms for detecting a definite Hermitian matrix pair

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