hw8 - to solve the system of two nonlinear equations above....

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Homework 8 Foundations of Computational Math 1 Fall 2011 The solutions will be posted on Friday, 12/2/11 Problem 8.1 Textbook, page 330, Problem 6 Problem 8.2 Consider the system of equations in R 2 ξ 2 + η 2 = 4 e ξ + η = 1 The system has two solutions in R 2 , one with ξ > 0 and η < 0 and one with ξ < 0 and η > 0. (8.2.a) Derive the iteration for Newton’s method to solve the system of two nonlinear equations above. Your document should include the iteration’s derivation. (8.2.b) Implement it and consider the performance for a variety of initial conditions to solve the system of two nonlinear equations above. (8.2.c) Derive an iteration using Nonlinear Jacobi-Newton (one-step) to solve the sys- tem of two nonlinear equations above. (8.2.d) Implement it and consider the performance for a variety of initial conditions
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Unformatted text preview: to solve the system of two nonlinear equations above. (8.2.e) Derive an iteration using Nonlinear Gauss-Seidel-Newton (one-step) to solve the system of two nonlinear equations above. (8.2.f) Implement it and consider the performance for a variety of initial conditions to solve the system of two nonlinear equations above. (8.2.g) Compare to the work required to achieve a given accuracy Nonlinear Jacobi-Newton and Gauss-Seidel-Newton, and Newtons Method when starting at the same initial condition? Also compare to iterations 1 and 2 in the latest program-ming assignment. Note you do not have to turn in any implementation. This is not a programming assign-ment. 1...
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