Review The Newton method and how it works where bisection - PowerPoint PPT Presentation

Numerical and Scientific Computing with Applications David F . Gleich CS 314, Purdue November 30, 2016 In this class: Review • The Newton method and how it works where bisection cannot! Next class • The Secant method and how it avoids needing the MIDTERM 3 derivatives that Newton’s requires. • The fixed-point form of the nonlinear equation Next next class problem. Topics 1 • List of topics • Selected problems from HW

Background I assume Linear algebra Calculus Differential equations Discrete math Programming Probability I’ll try to remind you what you need to know

Topics we’ve covered Week 10 Combinations of floating equations point error and Intro to Applied Math Forward Euler truncation error Function representations Local truncation error Richardson extrapolation Polynomial interpolation Consistency Errors in polynomial Lagrange polynomials Convergence interpolation Barycentric form Stability High dimensional Vandermonde matrix Absolute stability polynomials Piecewise polynomials Backwards Euler Week 12 ApproxFun Runge-Kutta Numerical integration Week 11 Week 14 Quadrature Numerical differentiation Nonlinear equations Trapezoidal rule Truncation error for Bisection Composite trapezoidal numerical differentiation Newton’s method rules Errors in forward difference Secant method Week 13 Errors in central difference Fixed Point methods Ordinary differential