Journal ArticleDOI
On the singular two-parameter eigenvalue problem ∗
Andrej Muhič,Bor Plestenjak +1 more
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TLDR
It is shown that the simple finite regular eigenvalues of a two-parameter eigen value problem and the associated system of generalized eigenvalue problems agree.Abstract:
In the 1960s, Atkinson introduced an abstract algebraic setting for multiparameter eigenvalue problems. He showed that a nonsingular multiparameter eigenvalue problem is equivalent to the associated system of generalized eigenvalue problems. Many theoretical results and numerical methods for nonsingular multiparameter eigenvalue problems are based on this relation. In this paper, the above relation to singular two-parameter eigenvalue problems is extended, and it is shown that the simple finite regular eigenvalues of a two-parameter eigenvalue problem and the associated system of generalized eigenvalue problems agree. This enables one to solve a singular two-parameter eigenvalue problem by computing the common regular eigenvalues of the associated system of two singular generalized eigenvalue problems.read more
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Functional Characterization of Intrinsic and Extrinsic Geometry
TL;DR: A novel way to capture and characterize distortion between pairs of shapes by extending the recently proposed framework of shape differences built on functional maps, and demonstrates that a set of four operators is complete, capturing intrinsic and extrinsic structure and fully encoding a shape up to rigid motion in both discrete and continuous settings.
Journal ArticleDOI
On linearizations of the quadratic two-parameter eigenvalue problems
TL;DR: In this paper, the quadratic two-parameter eigenvalue problem (QMEP) is transformed into a nonsingular five-parameters eigen value problem.
On linearizations of the quadratic two-parameter eigenvalue problems
TL;DR: In this article, the quadratic two-parameter eigenvalue problem (QMEP) is solved by formulating an associated linear multiparameter Eigenvalue (MLE) problem.
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Computing all Pairs (λ,μ) Such That λ is a Double Eigenvalue of A+μB
TL;DR: A method to accurately find all scalar pairs (λ,μ) such that A+μB has a double eigenvalue λ, where A and B are given arbitrary complex matrices.
References
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Journal ArticleDOI
Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation
TL;DR: The structure and design of the software package PHC is described, which features great variety of root-counting methods among its tools and is ensured by the gnu-ada compiler.
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The Computation of Kronecker's Canonical Form of a Singular Pencil
TL;DR: In this paper, stable algorithms for the computation of the Kronecker structure of an arbitrary pencil were developed, which can be viewed as a generalization of the wellknown eigenvalue problem of pencils of the type LambdaI-A.
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The generalized Schur decomposition of an arbitrary pencil A–lB—robust software with error bounds and applications. Part I: theory and algorithms
James Demmel,Bo Kågström +1 more
TL;DR: Robust software with error bounds for computing the generalized Schur decomposition of an arbitrary matrix pencil A – λB (regular or singular) is presented.