The Solution of Nonlinear Equations via the Method of Hurwitz-Radon Matrices

• 作者: Dariusz Jacek Jakóbczak
• 来源期刊: 电脑和通信(英文)
• 学科: 数学
• 关键词: Image Analysis Nonlinear Equation Root of Function CURVE INTERPOLATION Hurwitz-Radon
• 年，卷（期）: 2014,（10）
• 页码范围: 9-16
• 页数: 8页
• 分类号: O1

摘要

Image analysis and computer vision are interested in suitable methods to solve the nonlinear equations. Coordinate x??for f (x)?= 0?is crucial because each equation can be transformed into f (x)?= 0. A novel method of Hurwitz-Radon Matrices (MHR) can be used in approximation of a root of function in the plane. The paper contains a way of data approximation via MHR method to solve any equation. Proposed method is based on the family of Hurwitz-Radon (HR) matrices. The matrices are skew-symmetric and possess columns composed of orthogonal vectors. The operator of Hurwitz-Radon (OHR), built from these matrices, is described. Two-dimensional data are represented by discrete set of curve??f points. It is shown how to create the orthogonal OHR operator and how to use it in a process of data interpolation. MHR method is interpolating the curve point by point without using any formula or function.