广义反三对角汉克尔矩阵的逆和行列式的数值计算

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-09-23 DOI:10.1016/j.cam.2025.117076

Xin Fan, Ji-Teng Jia

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引用次数: 0

摘要

研究了广义反三对角汉克尔矩阵的逆矩阵和行列式。我们首先基于张量积和一般反三对角汉克尔矩阵的逆，给出了这些矩阵的逆的显式公式。然后提出了一种有效的矩阵反演算法，减少了存储这些矩阵的内存需求，并通过利用张量积的性质简化了分析。此外，我们还引入了一种计算广义反三对角Hankel矩阵行列式的高效算法，将其转化为求解低阶反三对角Hankel矩阵行列式的问题。我们还推导出行列式求值的显式公式。MATLAB仿真的数值结果证明了所提算法的准确性、效率和性能，并与MATLAB内置函数进行了比较，在计算精度和速度方面显示出明显的优势。

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On numerical computation of inverses and determinants for generalized anti-tridiagonal Hankel matrices

This paper investigates the inverses and determinants of generalized anti-tridiagonal Hankel matrices. We first present an explicit formula for the inverses of these matrices, based on tensor products and the inverses of general anti-tridiagonal Hankel matrices. An efficient algorithm for matrix inversion is then proposed, reducing memory requirements for storing these matrices and simplifying analysis by leveraging the properties of tensor products. Additionally, we introduce a cost-effective algorithm for computing the determinants of generalized anti-tridiagonal Hankel matrices, transforming the problem into that of lower-order anti-tridiagonal Hankel matrix determinants. We also derive an explicit formula for determinant evaluation. Numerical results from MATLAB simulations demonstrate the accuracy, efficiency, and performance of the proposed algorithms, which are compared to MATLAB built-in functions, showing clear advantages in computational accuracy and speed.

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.