基于广义下降梯度法的符合分数阶导数算法的计算性能

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED Journal of Computational and Applied Mathematics Pub Date : 2025-07-01 Epub Date: 2025-01-03 DOI:10.1016/j.cam.2024.116480

Marcio Antônio de Andrade Bortoloti

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引用次数: 0

摘要

在本文中，我们进行了下降梯度法（DGM）在符合分数阶导数的背景下的分析。探讨了具有连续Lipschitz梯度的函数的数学性质。值得注意的是，与传统的DGM相比，这种分数阶导数方法显着减少了计算工作量。此外，我们给出了一个详细的数值例子来证明该广义DGM算法的高性能。

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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Computational performance of a generalized descent gradient method based algorithm with conformable fractional-order derivatives

In this paper, we perform an analysis of the Descent Gradient Method (DGM) within the context of the conformable fractional derivatives. We explore the mathematical properties of functions with continuous Lipschitz gradients. Notably, this fractional derivative approach significantly reduced computational effort when compared to the conventional DGM. Additionally, we present a detailed numerical example to prove the high performance of this generalized DGM algorithm.

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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.