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New Matrix Inversion Algorithms Based on Exchange Method
October 1973 (vol. 22 no. 10)
pp. 885-890
R.M.-M. Chen, Bell Laboratories
This paper derives a set of new algorithms based on the exchange method for the computation of matrix inverses including nonsingular, symmetric nonsingular, and rectangular matrices. The symmetric matrix inversion algorithm can save up to 50 percent of the computation time required for the Gauss-Jordan elimination method. The pseudoinverse algorithms derived here are very attractive in terms of small storage requirement, short computation time, and high numerical accuracy. Comparisons are made between the new algorithms and existing ones, and numerical examples are included.
Index Terms:
Exchange method, generalized inverse of matrix, least squares solution, matrix decomposition, permutation, pivot selection, rank of matrix, symmetric matrix inversion.
Citation:
R.M.-M. Chen, "New Matrix Inversion Algorithms Based on Exchange Method," IEEE Transactions on Computers, vol. 22, no. 10, pp. 885-890, Oct. 1973, doi:10.1109/T-C.1973.223613
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