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Newton method; matrix inverse square root; iterative process
This paper is motivated by the paper [3], where an iterative method for the computation of a matrix inverse square root was considered. We suggest a generalization of the method in [3]. We give some sufficient conditions for the convergence of this method, and its numerical stabillity property is investigated. Numerical examples showing that sometimes our generalization converges faster than the methods in [3] are presented.
[1] A.J. Hoffman, K. Fan: Some metric inequalities in the space of matrices. Proc. Amer. Math. Soc. 6 (1955), 111–116. DOI 10.1090/S0002-9939-1955-0067841-7 | MR 0067841
[2] P. Lancaster: Theory of Matrices. Academic Pres, New York, 1969. MR 0245579 | Zbl 0186.05301
[3] N. Sherif: On the computation of a matrix inverse square root. Computing 46 (1991), 295–305. DOI 10.1007/BF02257775 | MR 1129098 | Zbl 0741.65039
[4] G.W. Stewart: Introduction to Matrix Computation. Academic Pres, New York, 1974. MR 0458818
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