Evaluation of Symbolic Expression of the First Derivative of Determinant
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概要
- 論文の詳細を見る
A method to evaluate the first derivative of the determinant of a given matrix of symbolic elements is considered. If evaluations such as substitution of numbers or a parameter for variables reduce the total number of variables, the determinant expansion can be made efficient by performing such evaluation elementwise before expansion, however, if the derivative of the determinant is required, we cannot perform such substitution for the differentiation variable in each matrix element. In this paper, we introduce a new operator ddet in order to solve this problem, and express these computational processes in terms of the operator. Given two matrices, the ddet operator computes the sum of the determinants of matrices constructed from the elements of both matrices, and, specially if one of the matrices is of derivative elements of the other, gives the first derivative of the determinant of the matrix. Also presented in this paper are efficient algorithms for ddet in terms of inductive formulas, where the recalculations of common subexpressions are eliminated. The algorithms are natural extensions of the known algorithms; minor expansion, Bareiss's Gaussian elimination, and, for polynomial cases, the interpolation algorithms. Finally, as an empirical study, we give a model of matrices, which appear when solving a system of algebraic equations by a general elimination method, and indicate the choice of the algorithm suited for our particular application, showing the effectiveness of our new operator as well.
- 一般社団法人情報処理学会の論文
- 1992-10-31
著者
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Kobayashi Hidetsune
Department Of Mathematics College Of Science And Technology Nihon University
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Murao H
Computer Centre University Of Tokyo
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Murao Hirokazu
Computer Centre The University Of Tokyo
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FUJISE TETSURO
ICOT.
関連論文
- Evaluation of Symbolic Expression of the First Derivative of Determinant
- Implementation and Experiments of Faster Algorithms for Integer GCD's inRisa/Asir