On the least squares solution of inverse eigenvalue problems
, 1996 . An inverse eigenvalue problem, where a matrix is to be constructed from some or all of its eigenvalues, may not have areal-valued solution at all. An approximate solution in the sense of least squares is sometimes desirable.
Moody, T. Chu, Xuzhou Chen
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An Evaluation of Software for Computing Eigenvalues of Sparse Nonsymmetric Matrices
, 1996 The past few years have seen a significant increase in research into numerical methods for computing selected eigenvalues of large sparse nonsymmetric matrices. This research has begun to lead to the development of high-quality mathematical software. The
J. A. Scott, R.B. Lehoucq
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Bounds for the Z-spectral radius of nonnegative tensors. [PDF]
Springerplus, 2016 He J, Liu YM, Ke H, Tian JK, Li X.
europepmc +1 more source
Error Analysis of the Lanczos Algorithm for the Nonsymmetric Eigenvalue Problem
, 1994 This paper presents an error analysis of the Lanczos algorithm in finite precision arithmetic for solving the standard nonsymmetric eigenvalue problem, if no breakdown occurs.
Zhaojun Bai
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New inclusion sets for singular values. [PDF]
J Inequal Appl, 2017 He J, Liu YM, Tian JK, Ren ZR.
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Lanczos Methods For The Solution Of Nonsymmetric Systems Of Linear Equations
, 1992 . The Lanczos or biconjugate gradient method is often an effective means for solving nonsymmetric systems of linear equations. However, the method sometimes experiences breakdown, a near division by zero which may hinder or preclude convergence.
Wayne Joubert
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RADI: a low-rank ADI-type algorithm for large scale algebraic Riccati equations. [PDF]
Numer Math (Heidelb), 2018 Benner P +3 more
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A Stable Numerical Method For Inverting Shape From Moments
, 1997 . We derive a stable technique, based upon matrix pencils, for the reconstruction of (or approximation by) polygonal shapes from moments. Wepoint out that this problem can be considered the dual of 2 ; D numerical quadrature over polygonal domains.
Peyman Milanfar +2 more
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Randomized algorithms for distributed computation of principal component analysis and singular value decomposition. [PDF]
Adv Comput Math, 2018 Li H, Kluger Y, Tygert M.
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An Overview Of Relative sin Theta Theorems For Invariant Subspaces Of Complex Matrices
, 2007 . Relative perturbation bounds for invariant subspaces of complex matrices are reviewed, with emphasis on bounding the sines of the largest principal angle between two subspaces, i.e. sin \Theta theorems.
Ilse C. F. Ipsen
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