Skip to main content
Article
Solving Nonlinear Systems of Equations With Only One Nonlinear Variable
Journal of Computational and Applied Mathematics (1990)
  • Tjalling Ypma, Western Washington University
  • Yun-Qiu Shen, Western Washington University
Abstract
We describe a method for solving systems of N + 1 nonlinear equations in N + 1 unknowns y \te; ℝ and z \te; ℝN of the form A(y)z + b(y) = 0, where the (N + 1) × N matrix A(y) and vector b(y) are functions of y alone. Such equations arise in minimax approximation. We reduce the problem to one equation in y only. An efficient quadratically convergent numerical technique based on Newton's method in one variable is used to solve this equation. Computational details and results are provided, and two generalizations are discussed.
Keywords
  • Nonlinear equations,
  • Newton's method,
  • minimax approximation,
  • Remez algorithm
Disciplines
Publication Date
May 28, 1990
Publisher Statement
Copyright © 1990 Published by Elsevier B.V. doi:10.1016/0377-0427(90)90031-T
Citation Information
Tjalling Ypma and Yun-Qiu Shen. "Solving Nonlinear Systems of Equations With Only One Nonlinear Variable" Journal of Computational and Applied Mathematics Vol. 30 Iss. 2 (1990)
Available at: http://works.bepress.com/tjalling_ypma/19/