Numerical Methods for Inverting Positive Definite Matrices

R. J. Clasen

ResearchPublished 1966

An explanation of four methods for inverting positive definite matrices: the Gauss-Jordan and bordering methods, the square root procedure, and the Choleski method. The theory of positive definite matrices is summarized, and main applications of the matrices are discussed. A comparison of the accuracy of the inversion techniques is also made. Major conclusions are that matrices in many applications can be shown to be positive definite or partitionable into definite submatrices and, hence, can be inverted by means of special algorithms; and that Choleski's method is faster and seems at least as accurate as the more common methods for solving simultaneous equations.

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Clasen, R. J., Numerical Methods for Inverting Positive Definite Matrices. Santa Monica, CA: RAND Corporation, 1966. https://www.rand.org/pubs/research_memoranda/RM4952.html.
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