A nonlinear Filbert-like matrix with three free parameters: From linearity to nonlinearity

IF 0.9 3区数学 Q2 MATHEMATICS

Mathematica Slovaca Pub Date : 2024-07-01 DOI:10.1515/ms-2024-0044

Emrah Kiliç, Didem Ersanli

引用次数: 0

Abstract

Filbert and Lilbert matrices are defined by terms of linear Fibonacci-like sequences. By considering terms of such linear recurrences and additional free parameters, we define a nonlinear variant of these matrices via ratios of q-forms of terms of Fibonacci-like sequences whose indices are in nonlinear forms. We derive explicit formulae for the matrices L and U come from LU-decomposition, their inverses, inverse of the main matrices and their determinants.

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具有三个自由参数的非线性菲尔伯特类矩阵：从线性到非线性

菲尔伯特矩阵和利尔伯特矩阵是由线性斐波那契类序列的项定义的。通过考虑这种线性递归的项和额外的自由参数，我们通过指数为非线性形式的斐波纳契类序列项的 q 形式比率定义了这些矩阵的非线性变体。我们从 LU 分解、它们的逆、主矩阵的逆和它们的行列式中推导出矩阵 L 和 U 的明确公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematica Slovaca 数学-数学

CiteScore

2.10

自引率

6.20%

发文量

审稿时长

6-12 weeks

期刊介绍： Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process. Its reputation was approved by many outstanding mathematicians who already contributed to Math. Slovaca. It makes bridges among mathematics, physics, soft computing, cryptography, biology, economy, measuring, etc.　 The Journal publishes original articles with complete proofs. Besides short notes the journal publishes also surveys as well as some issues are focusing on a theme of current interest.