A new family of means: the generalized weighted power means and applications. Issue 2 (1st February 2023)

• Record Type: Journal Article
• Authors: Amat, Sergio; Jiménez, Isabel; Ruiz, Juan; Carlos Trillo, Juan; Yáñez, Dionisio F.
• Is Part Of: International journal of computer mathematics. Volume 100:Issue 2(2023)
• Page Start: 422
• Page End: 439
• Publication Date: 2023-02-01
• Subjects: Weighted nonlinear means -- nonuniform meshes -- nonlinear subdivision schemes -- stability theorems -- conservation laws; 41A05 -- 41A10 -- 65D17; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2022.2120353
• Languages: English
• ISSNs: 0020-7160

Abstract

Abstract : Our aim is to define a new mean having specific properties which are crucial in several applications. As examples of this kind of applications, we can mention subdivision and multiresolution schemes based on nonuniform meshes and the numerical solution of conservation laws. Specifically, we pay attention to three relevant properties: to remain close to the minimum of the two values, to give a closer value to the weighted arithmetic mean of the two values when they are already similar, and to accomplish a Lipchitz condition. We define a family of means depending on a parameter k that matches these requirements. Using these means, it is possible to obtain more accurate theoretical constants in some stability theorems, and therefore they are better fitted to what happens in real examples. We carry out examples in the fields of subdivision schemes and hyperbolic conservation laws.