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1

Inversion of selected structures of block matrices of chosen mechatronic systems

Trawiński T., Kochan A., Kielan P., Kurzyk D.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2016

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Vol. 64, nr 4

853--863

EN

This paper describes how to calculate the number of algebraic operations necessary to implement block matrix inversion that occurs, among others, in mathematical models of modern positioning systems of mass storage devices. The inversion method of block matrices is presented as well. The presented form of general formulas describing the calculation complexity of inverted form of block matrix were prepared for three different cases of division into internal blocks. The obtained results are compared with a standard Gaussian method and the “inv” method used in Matlab. The proposed method for matrix inversion is much more effective in comparison in standard Matlab matrix inversion “inv” function (almost two times faster) and is much less numerically complex than standard Gauss method.

2

A new method for solving ill-conditioned linear systems

Soleymani F.

Opuscula Mathematica

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2013

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Vol. 33, no. 2

337--344

EN

An accurate numerical method is established for matrix inversion. It is shown theoretically that the scheme possesses the high order of convergence of seven. Subsequently, the method is taken into account for solving linear systems of equations. The accuracy of the contributed iterative method is clarified on solving numerical examples when the coefficient matrices are ill-conditioned. All of the computations are performed on a PC using several programs written in MATHEMATICA 7.

3

Odwracanie macierzy o wybranych strukturach przy pomocy macierzy blokowych

Trawiński T.

Przegląd Elektrotechniczny

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2009

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R. 85, nr 6

98-101

PL

W niniejszym artykule przedstawiono metodę odwracania macierzy bezwładnościowych. Prezentowane macierze bezwładnościowe mają cechy symetrii charakterystyczne dla macierzy spotykanych w przetwornikach elektromechanicznych, bądź w robotyce w modelowaniu dynamiki manipulatorów robotów. Prezentowana metoda nadaje się do formułowania równań modeli matematycznych rozgałęzionych łańcuchów kinematycznych systemów pozycjonowania głowic pamięci masowych.

EN

In this article inversion method of inertial matrices is presented. Presented inertial matrices has similar structure to these which occur in electromechanical devices (such induction motors) or in robotics, in mathematical modeling of manipulators dynamics. Presented method is very helpful in mathematical equation formulation of branched positioning head system of mass storage devices.

4

Inversion of Square Matrices in Processors With Limited Calculation Abillities

Janiszowski K. B.

International Journal of Applied Mathematics and Computer Science

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2003

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Vol. 13, no 2

199-204

EN

An iterative inversion algorithm for a class of square matrices is derived and tested. The inverted matrix can be defined over both real and complex fields. This algorithm is based only on the operations of addition and multiplication. The numerics of the algorithm can cope with a short number representation and therefore can be very useful in the case of processors with limited possibilities, like different neuro-computers and accelerator cards. The quality of inversion can be traced and tested. The algorithm can be used in the case of singular matrices, and then it automatically produces a result that contains the inverse of this part of the processed matrix which can be inverted. An example of the inversion of a six-order square matrix is presented and discussed.