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Completion method

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A method for calculating the inverse of a matrix, based on a recurrent transition which involves the calculation of a matrix , where is a column vector, is a row vector, by the formula

The computational scheme of the method is as follows. Let be a given matrix of order . Consider a sequence , where , is the -th column of the identity matrix , . Then and the matrix is obtained by applying the above-described procedure times. The computational formulas in this case are the following: If is the -th column of , then for ,

(*)

It is sufficient to compute the elements of the first rows of the matrix , since all subsequent rows coincide with the rows of the identity matrix.

Other possibilities of arranging the computations in the completion method based on certain modifications of (*) are known, e.g. the so-called Ershov method (see [1]).

References

[1] D.K. Faddeev, V.N. Faddeeva, "Computational methods of linear algebra" , Freeman (1963) (Translated from Russian)


Comments

This method is also called the bordering method (cf. [1]). See, however, also Bordering method.

How to Cite This Entry:
Completion method. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Completion_method&oldid=39782
This article was adapted from an original article by G.D. Kim (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article