Numerical Analysis I

Catalog description

Approximation and interpolation, numerical quadrature, direct methods of numerical linear algebra, numerical solutions of nonlinear systems and optimization. MATH 523 Numerical Analysis I (3) 1. Approximation and interpolation. Weierstrass theorem, Bernstein polynomials, Jackson theorems, Lagrange interpolation, least squares approximation, orthogonal polynomials, piecewise Lagrange and Hermite interpolation, spline interpolation, the Fast Fourier Transform.2. Numerical quadrature. Newton-Cotes rules, Peano Kernel Theorem, Euler-Maclaurin expansion, Romberg integration, Gaussian quadrature, adaptive quadrature.3. Direct methods of numerical linear algebra. Gaussian elimination with pivoting, backward error analysis, conditioning of linear systems.4. Numerical solution of nonlinear systems and optimization. One-point iterations, Newton's and quasi-Newton's method, Broyden's method, unconstrained optimization, line-search methods.