Computational Efficiency for Calculating Determinants of Block Matrices
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Abstract
In this paper, we study a method for calculating the determinant of a matrix divided into four submatrices using the formula of Schur. The purpose of this study is to analyze and provide the formula for the number of flops for matrix determinants consisting of submatrices of different sizes. The results are analyzed based on matrices with a submatrix on the first main diagonal of size . It shows that using the formula of Schur to calculate the determinant gives the number of flops close to calculating the determinant directly using the Gaussian elimination method. We also prove the relationship between the number of flops of determinant calculations by using the formula of Schur and direct determinant calculations using the Gaussian elimination method. Numerical experiments are presented, and the conclusions of the theoretical analysis are well supported.
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ลิขสิทธ์ ของมหาวิทยาลัยเทคโนโลยีราชมงคลพระนครReferences
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