Fast computing of the Moore-Penrose inverse matrix

Katsikis, Vasilios N.; Pappas, Dimitrios

doi:10.13001/1081-3810.1287

Cited by 35 publications

(45 citation statements)

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“…They are available in standard libraries, such as LAPACK and Matlab. Nevertheless this area of research is very active and some authors propose methods of computing A † based on the formula A † = (A T A) −1 A T (see, e.g., [6,[16][17][18][19]), where the matrix A T A is formed explicitly. This algorithm may be fast, compared to the SVD decomposition, it is well known however, that for ill-conditioned matrices this approach may lead to severe loss of accuracy.…”

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confidence: 99%

Numerical aspects of computing the Moore-Penrose inverse of full column rank matrices

Smoktunowicz

Wróbel

2011

Bit Numer Math

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This paper presents a comparison of certain direct algorithms for computing the Moore-Penrose inverse, for matrices of full column rank, from the point of view of numerical stability. It is proved that the algorithm using Householder QR decomposition, implemented in floating point arithmetic, is forward stable but only conditionally mixed forward-backward stable. A similar result holds also for the Classical Gram-Schmidt algorithm with reorthogonalization (CGS2). This algorithm was developed and analyzed by Abdelmalek (BIT, 11 (4) We incorporate the recent result of Byers and Xu (SIAM J. Matrix Anal. Appl. 30:822-843, 2008) to show that the algorithm based on the Golub-Kahan bidiagonalization is mixed forward-backward stable under natural assumptions.

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confidence: 99%

Numerical aspects of computing the Moore-Penrose inverse of full column rank matrices

Smoktunowicz

Wróbel

2011

Bit Numer Math

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“…In [9], based on Theorem 1, the authors developed an algorithm (the ginv function) for computing the generalized inverse of full rank matrices, and of square matrices with at least one zero row or column and the rest of the matrix full rank. In other words, our main concern was to calculate the corresponding k i in the expansion Table 11 Error and Computational Time Results; matrix market sparse matrices.…”

Section: The Computational Methodsmentioning

confidence: 99%

“…In a recent article [9], the first two authors provided a new method for the fast computation of the generalized inverse of full rank rectangular matrices and of square matrices with at least one zero row or column. In order to reach this goal, a special type of tensor product of two vectors was used, usually defined in infinite dimensional Hilbert spaces.…”

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confidence: 99%

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An improved method for the computation of the Moore–Penrose inverse matrix

Katsikis

Pappas

Petralias

2011

Applied Mathematics and Computation

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“…The topic of ELMs is subject to discussion as they are considered similar to, or special cases of, radial basis function (RBF) networks, random vector functional-link (RVFL), least squares support vector machines (LS-SVM), or reduced SVM [11] [12] [13]. In this paper, networks constructed as indicated above, were trained using different approaches for the computation of the Moore-Penrose pseudoinverse (using Singular Value Decomposition and the algorithms described in [14], [15]). …”

Section: B Extreme Learning Machinesmentioning

confidence: 99%

Towards conservative helicopter loads prediction using computational intelligence techniques

Valdés

Cheung

2012

The 2012 International Joint Conference on Neural Networks (IJCNN)

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Vous avez des questions? Nous pouvons vous aider. Pour communiquer directement avec un auteur, consultez la première page de la revue dans laquelle son article a été publié afin de trouver ses coordonnées. Si vous n'arrivez pas à les repérer, communiquez avec nous à PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca. Questions? Contact the NRC Publications Archive team atPublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca. If you wish to email the authors directly, please see the first page of the publication for their contact information. NRC Publications Archive Archives des publications du CNRCThis publication could be one of several versions: author's original, accepted manuscript or the publisher's version. / La version de cette publication peut être l'une des suivantes : la version prépublication de l'auteur, la version acceptée du manuscrit ou la version de l'éditeur. NRC Publications Record / Notice d'Archives des publications de CNRC:http://nparc.cisti-icist.nrc-cnrc.gc.ca/eng/view/object/?id=10db696b-8a8c-4547-b93c-48837b7cb311 http://nparc.cisti-icist.nrc-cnrc.gc.ca/fra/voir/objet/?id=10db696b-8a8c-4547-b93c-48837b7cb311Towards conservative helicopter loads prediction using computational intelligence techniques Abstract-Airframe structural integrity assessment is a major activity for all helicopter operators. The accurate estimation of component loads is an important element in life cycle management and life extension efforts. This paper explores continued efforts to utilize a wide variety of computational intelligence techniques to estimate some of these helicopter dynamic loads. Estimates for two main rotor sensors (main rotor normal bending and pushrod axial load) on the Australian Black Hawk helicopter were generated from an input set that consisted of thirty standard flight state and control system parameters. These estimates were produced for two flight conditions: full speed forward level flight and left rolling pullout at 1.5g. Two sampling schemes were attempted, specifically k-leaders sampling and a biased sampling scheme. Ensembles were constructed from the top performing models that used conjugate gradient, LevenbergMarquardt (LM), extreme learning machines, and particle swarm optimization (PSO) as the learning method. Hybrid and memetic approaches combining the deterministic optimization and evolutionary computation techniques were also explored. The results of this work show that using a biased sampling scheme significantly improved the predictions, particularly at the peak values of the target signal. Hybrid models using PSO and LM learning provided accurate and correlated predictions for the main rotor loads in both flight conditions.

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Fast computing of the Moore-Penrose inverse matrix

Cited by 35 publications

References 6 publications

Numerical aspects of computing the Moore-Penrose inverse of full column rank matrices

Numerical aspects of computing the Moore-Penrose inverse of full column rank matrices

An improved method for the computation of the Moore–Penrose inverse matrix

Towards conservative helicopter loads prediction using computational intelligence techniques

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