MthSc 860
Spring 2007
Review for Exam 2
V. Nonlinear Equations (Heath Ch. 5)
Iterative Methods
Convergence rate
Termination criteria
Bisection
Fixed-Point Iteration
Newton's Method
Secant Method
Inverse Quadratic Interpolation
Systems of Nonlinear Equations
Fixed-Point Iteration
Newton's Method
VII. Interpolation (Heath Ch. 7)
Polynomial Interpolation
Vandermonde (monomial) approach
Nested multiplication
Lagrange Form
Newton Form
Nested multiplication
Divided Differences
Accuracy
Piecewise Polynomial Interpolation
Continuous pw linear, quadratic, cubic
Splines
General definition
Cubic
Endpoint conditions
VIII. Numerical Integration (Heath Ch. 8)
Newton-Cotes
Midpoint, Trapezoid, Simpson's
Accuracy
Polonomial Degree
Open vs. closed
Gaussian Quadrature
Gauss-Legendre
Weighted Integrals
Composite Quadrature Rules
Error (convergence rates)
Adaptive Quadrature
Using Matlab quad routine