JOURNAL ARTICLE

New smoothing function for solving absolute value equations.

  • Published In: Asian-European Journal of Mathematics, 2023, v. 16, n. 12. P. 1 1 of 3

  • Database: Mathematics Source 2 of 3

  • Authored By: Chalekh, Randa; Djeffal, El Amir 3 of 3

Abstract

In this paper, we use a smoothing-type algorithm in this paper to solve the AVE, which stands for the absolute value equation A x − | x | = b , where A is an arbitrary n × n real matrix and b ∈ ℝ n . We reformulate AVE as a system of smooth equations and propose two new smoothing functions. We prove that the algorithm is well-defined when the singular value of A exceeds one, and under the same assumption, the algorithm is convergent. We show the algorithm's effectiveness with these two functions and compare it with some previously known functions. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Asian-European Journal of Mathematics. 2023/12, Vol. 16, Issue 12, p1
  • Document Type:Article
  • Subject Area:Science
  • Publication Date:2023
  • ISSN:1793-5571
  • DOI:10.1142/S1793557123502261
  • Accession Number:174689186
  • Copyright Statement:Copyright of Asian-European Journal of Mathematics is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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