Solution of the Generalized Abel Integral Equation by Using Almost Bernstein Operational Matrix

• 作者: Om P. Singh Rajesh K. Pandey Sandeep Dixit Sunil Kumar
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: ABEL INVERSION BERNSTEIN POLYNOMIALS ALMOST BERNSTEIN OPERATIONAL Matrix Of Integration Noise Resistance
• 年，卷（期）: 2011,（4）
• 页码范围: 226-234
• 页数: 9页
• 分类号: O1

摘要

A direct almost Bernstein operational matrix of integration is used to propose a stable algorithm for numerical inversion of the generalized Abel integral equation. The applicability of the earlier proposed methods was restricted to the numerical inversion of a part of the generalized Abel integral equation. The method is quite accurate and stable as illustrated by applying it to intensity data with and without random noise to invert and compare it with the known analytical inverse. Thus it is a good method for applying to experimental intensities distorted by noise.