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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Fall 2003 • Question 1

Question

Math 6610 • Analysis of Numerical Methods I Fall 2003 • Question 1

Newton’s Method Describe how (the two-variable version of) Newton’s Method can be used to solve the nonlinear system \[ \begin {aligned} x^2+y^2 &= 1,\\ e^x-y &= 0 \end {aligned} \tag {1} \] Discuss the selection of a starting point and the advantages and disadvantages of Newton’s method.

Raw LaTeX

{Newton's Method}
Describe how (the two-variable version of) Newton's Method can be used to solve the
nonlinear system
\[
\begin{aligned}
  x^2+y^2 &= 1,\\
  e^x-y &= 0
\end{aligned}
\tag{1}
\]
Discuss the selection of a starting point and the advantages and disadvantages of
Newton's method.

Topic Tags

Iterative Methods for Linear Systems Linear Programming and Optimization Variable-Coefficient Diffusion Problems