Derivative of a Determinant with Respect to an Eigenvalue in the <i>LDU</i>Decomposition of a Non-Symmetric Matrix

• 作者: Mitsuhiro Kashiwagi
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: DERIVATIVE of DETERMINANT Non-Symmetric MATRIX EIGENVALUE Band MATRIX LDU DECOMPOSITION
• 年，卷（期）: yysxyw_2013,（3）
• 页码范围: 464-468
• 页数: 5页
• 分类号: O1

摘要

We demonstrate that, when computing the LDU decomposition (a typical example of a direct solution method), it is possible to obtain the derivative of a determinant with respect to an eigenvalue of a non-symmetric matrix. Our proposed method augments an LDU decomposition program with an additional routine to obtain a program for easily evaluating the derivative of a determinant with respect to an eigenvalue. The proposed method follows simply from the process of solving simultaneous linear equations and is particularly effective for band matrices, for which memory requirements are significantly reduced compared to those for dense matrices. We discuss the theory underlying our proposed method and present detailed algorithms for implementing it.