Numerical algorithms for the Moore-Penrose inverse of a matrix: Direct methods

Shinozaki, Nobuo; Sibuya, Masaaki; Tanabe, Kunio

doi:10.1007/bf02479751

Cited by 52 publications

(24 citation statements)

References 14 publications

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“…Hüls (2008). For the computation of the Moore-Penrose inverse, we refer to Shinozaki et al (1972). The dichotomy projector is the N-th block component of the solution u J .…”

Section: Numerical Detection Of Sacker-sell Spectral Intervals Via DImentioning

confidence: 99%

Computing Sacker–Sell spectra in Discrete Time Dynamical Systems

Hüls¹

2010

SIAM J. Numer. Anal.

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In this paper we develop two boundary value methods for detecting SackerSell spectra in discrete time dynamical systems. The algorithms are advancements of earlier methods for computing projectors of exponential dichotomies. The first method is based on the projector residual P P − P . If this residual is large, then the difference equation has no exponential dichotomy. A second criterion for detecting Sacker-Sell spectral intervals is the norm of end points of the solution of a specific boundary value problem. Refined error estimates for the underlying approximation process are given and the resulting algorithms are applied to an example with known continuous Sacker-Sell spectrum, as well as to the variational equation along orbits of Hénon's map.

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“…Hüls (2008). For the computation of the Moore-Penrose inverse, we refer to Shinozaki et al (1972). The dichotomy projector is the N-th block component of the solution u J .…”

Section: Numerical Detection Of Sacker-sell Spectral Intervals Via DImentioning

confidence: 99%

Computing Sacker–Sell spectra in Discrete Time Dynamical Systems

Hüls¹

2010

SIAM J. Numer. Anal.

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“…There are many methods to compute the Moore-Penrose inverse of a matrix. Shinozaki et al(1972aShinozaki et al( , 1972b surveyed the methods for computing the Moore-Penrose inverse into two subjects: direct methods and iterative methods. In order to find the Moore-Penrose inverse of an arbitrary matrix, these methods are very useful.…”

Section: Introductionmentioning

confidence: 99%

The Orthogonal Projection Matrix for the Unbalanced Factorial Design

Kim

Park

1992

Journal of the Japanese Society of Computational Statistics

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“…For the calculation of the pseudoinverse there exists a numerically more efficient approach using Singular Value Decomposition (SVD), see [147]. is fulfilled [132].…”

Section: A2 Gridded Data Interpolationmentioning

confidence: 99%