Inverting a positive definite matrix: A comparative study of two algorithms
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The purpose of the paper is to investigate the efficiency of two matrix-inverting algorithms that are restricted to positive definite matrices. The selected algorithms are a Guass-Jordan method and a gradient projection optimization scheme. To investigate the efficiency, we will be comparing the two algorithms and the two hardware systems. The primary system is a vonNeumann machine, specifically a PC. The other system is a parallel processor we have designed specifically for matrix inversion and implemented by simulation. The paper begins with a review of some basic results concerning positive definite matrices. Following this review, the paper describes the two mathematical algorithms used to determine the inverse and how they will be implemented on the PC. Next we describe the architecture of the parallel processor that will be used to simulate matrix inversion. Following the description of the parallel processor, the implementation of each algorithm on the parallel system is described. To test the efficiency of the algorithms we apply each to several large positive definite matrices and measure the time. The paper concludes with the results of the efficiency study in which each algorithm is compared on the selected system and each system is compared for the selected algorithm.