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

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

Emrah Kiliç, Didem Ersanli

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引用次数: 0

摘要

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。

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

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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