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Perturbation theory of eigenvalue problems
Franz Rellich,B. J. Berkowitz +1 more
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The article was published on 1969-01-01 and is currently open access. It has received 600 citations till now. The article focuses on the topics: Inverse iteration & Eigenvalue perturbation.read more
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Nondifferentiable optimization algorithm for designing control systems having singular value inequalities
Elijah Polak,Y. Wardi +1 more
TL;DR: This paper presents an optimization algorithm which permits all the constraints of control system design requirements to be considered, involving the singular values of a system or return difference transfer function matrix.
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Adaptive eigendecomposition of data covariance matrices based on first-order perturbations
TL;DR: In this paper, new algorithms for adaptive eigendecomposition of time-varying data covariance matrices are presented, based on a first-order perturbation analysis of the rank-one update for covariance matrix estimates with exponential windows.
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Generic properties of the eigenvalue of the laplacian for compact riemannian manifolds
Shigetoshi Bando,Hajime Urakawa +1 more
TL;DR: In this paper, the eigenvalues of the Laplacian for compact Riemannian manifolds without boundary were studied and a simple proof of the continuous dependence of the Dirichlet problem on variations of domains was given.
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Mathematical and Computational Methods in Photonics and Phononics
TL;DR: In this article, a review of fundamental mathematical tools, computational approaches, and inversion and optimal design methods to address challenging problems in photonics and phononics is presented, where an emphasis is placed on analyzing subwavelength resonators, super-focusing and super-resolution of electromagnetic and acoustic waves.
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Strain Rates and Material Spins
TL;DR: In this paper, the authors derived a simple formula for the gradient of the tensor-valued function defining a general class of strain measures and derived a basis-free expression for the material time rate of an arbitrary Lagrangean strain measure in terms of the right Cauchy-Green tensor.