Inversion of square matrices in processors with limited calculation abillities

Krzysztof Janiszowski

International Journal of Applied Mathematics and Computer Science (2003)

  • Volume: 13, Issue: 2, page 199-204
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Janiszowski, Krzysztof. "Inversion of square matrices in processors with limited calculation abillities." International Journal of Applied Mathematics and Computer Science 13.2 (2003): 199-204. <http://eudml.org/doc/207636>.

@article{Janiszowski2003,
abstract = {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.},
author = {Janiszowski, Krzysztof},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {neuro-processors; matrix inversion; exponential matrix series},
language = {eng},
number = {2},
pages = {199-204},
title = {Inversion of square matrices in processors with limited calculation abillities},
url = {http://eudml.org/doc/207636},
volume = {13},
year = {2003},
}

TY - JOUR
AU - Janiszowski, Krzysztof
TI - Inversion of square matrices in processors with limited calculation abillities
JO - International Journal of Applied Mathematics and Computer Science
PY - 2003
VL - 13
IS - 2
SP - 199
EP - 204
AB - 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.
LA - eng
KW - neuro-processors; matrix inversion; exponential matrix series
UR - http://eudml.org/doc/207636
ER -

References

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  1. Beernaert L. and Roose D. (1991): Parallel Gaussian elimination, iPSC2 hypercube versus a transputer network, In: Numerical Linear Algebra (G. Golub, Ed.).- NATO ASI Series, Vol. 70, Berlin: Springer. Zbl0734.65013
  2. Bodewig E. (1965): Matrix Calculus. - Amsterdam: North-Holland. Zbl0086.32501
  3. Bjorck A. (1991): Error analysis of least squares algorithms, In: Numerical Linear Algebra (G. Golub, Ed.). - NATO ASI Series, Vol. 70, Berlin: Springer. Zbl0757.65047
  4. Collar A.R. and Simpson A. (1987): Matrices and Engineering Dynamics.- New York: Wiley. Zbl0701.65017
  5. Golub G., Greenbaum A. and Luskin M. (1992): Recent Advances in Iterative Methods.- New York: Springer. Zbl0790.00015
  6. Higham J.H. (1996): Accuracy and Stability of Numerical Algorithms. - Philadelphia: SIAM. Zbl0847.65010
  7. Kiełbasiński A. and Szczepik H. (1992): Numerical Algebra. - Warsaw: WNT, (in Polish). 
  8. Masters T. (1993): Practical Neural Network Recipes in C++. - London: Academic Press. Zbl0818.68049
  9. Synapse 3 (1977): PC Siemens Card- Technical Documentation. -Dresden: Siemens. 
  10. William H., Flannery B., Teukolsky S. and Vetterling W. (1992): Numerical Recipes in C. - New York: Cambrige University Press. Zbl0778.65003

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