Incomplete block‐matrix factorization of M ‐matrices using two‐step iterative method for matrix inversion and preconditioning

2020 ◽  
Author(s):  
S.C. Buranay ◽  
O.C. Iyikal
Keyword(s):  
Iterative Method ◽  
Matrix Factorization ◽  
Matrix Inversion ◽  
Block Matrix ◽  
Incomplete Block

Incomplete block-matrix factorization iterative methods for convection-diffusion problems

1989 ◽  
Vol 29 (4) ◽  
pp. 867-889 ◽  
Author(s):  
O. Axelsson ◽  
V. Eijkhout ◽  
B. Polman ◽  
P. Vassilevski
Keyword(s):  
Iterative Methods ◽  
Matrix Factorization ◽  
Block Matrix ◽  
Incomplete Block ◽  
Convection Diffusion ◽  
Diffusion Problems

scholarly journals A New High-Order Stable Numerical Method for Matrix Inversion

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
F. Khaksar Haghani ◽  
F. Soleymani
Keyword(s):  
Iterative Method ◽  
Numerical Method ◽  
Matrix Inversion ◽  
High Order ◽  
New Method ◽  
Order Convergence ◽  
Initial Value ◽  
Numerical Examples ◽  
Stable Numerical Method

A stable numerical method is proposed for matrix inversion. The new method is accompanied by theoretical proof to illustrate twelfth-order convergence. A discussion of how to achieve the convergence using an appropriate initial value is presented. The application of the new scheme for finding Moore-Penrose inverse will also be pointed out analytically. The efficiency of the contributed iterative method is clarified on solving some numerical examples.

scholarly journals Inversion of selected structures of block matrices of chosen mechatronic systems

2016 ◽  
Vol 64 (4) ◽  
pp. 853-863
Author(s):  
T. Trawiński ◽  
A. Kochan ◽  
P. Kielan ◽  
D. Kurzyk
Keyword(s):  
Matrix Inversion ◽  
Block Matrix ◽  
Inversion Method ◽  
Mass Storage ◽  
Mechatronic Systems ◽  
Positioning Systems ◽  
Block Matrices ◽  
Storage Devices ◽  
Gaussian Method ◽  
Gauss Method

AbstractThis 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.

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