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Solving N+m Nonlinear Equations with Only m Nonlinear Variables
Computing (1990)
  • Tjalling Ypma, Western Washington University
  • Yun-Qiu Shen, Western Washington University
We derive a method for solving N+m nonlinear algebraic equations in N+munknowns y≠R m and z≠R N of the form A(y)z+b(y)=0, where the(N+m) × N matrix A(y) and vector b(y) are continuously differentiable functions ofy alone. By exploiting properties of an orthonormal basis for null (AT(y)) the problem is reduced to solving m nonlinear equations in y only. These equations are solved by Newton's method inm variables. Details of computational implementation and results are provided.
  • Nonlinear equations,
  • null space,
  • continuous basis,
  • Newton's method
Publication Date
September, 1990
Publisher Statement
Published by Springer 10.1007/BF02262221
Citation Information
Tjalling Ypma and Yun-Qiu Shen. "Solving N+m Nonlinear Equations with Only m Nonlinear Variables" Computing Vol. 44 Iss. 3 (1990)
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