Numerical Analysis

Floating Point Arithmetic. Data and Function approximation methods with polynomials, splines, Bezier curves, trigonometric polynomials and Fourier series. Numerical methods for solving determined and over-determined linear equations (Least Square Methods). Numerical methods for nonlinear systems and applications to optimization problems. Numerical methods of eigenvalues ​​and eigenvectors approximation, SVD. Applications to problems of data compression and data mining. Numerical integration and differentiation. Solution methods for ordinary differential equations. Introduction to scientific programming with Matlab.

Objectives

The course aims to give students the necessary knowledge and tools to solve known mathematical problems arising directly problems from hardware and telecommunications (including solution of systems of linear and nonlinear equations, solution of differential equations, data approximation, etc.). MATLABsoftware, which is well known and used by engineers and computer scientists, makes it possible to implement and study the methods presented in theory. Upon successful completion of this course the student will : • Have a great understanding on how to solve linear systems by direct and iterative methods and will be able to choose the proper method per problem. • Have knowledge of basic methods of solving systems of nonlinear equations. • Have knowledge of data approximation and interpolation methods using polynomials/splines and/or trigonometric functions (Fourier). • Have knowledge in basic numerical methods of finite differences differentiation and integration, which will be extremely useful for the numerical solution of differential equations. • Be able to understand the effect of finite arithmetic errors and errorsof methods in numerical results. • Have basic knowledge of MATLAB software and its toolboxes.

Prerequisites

Programming I, Calculus I, Linear Algebra

Syllabus

Floating-point arithmetic. Methods of function and data approximation with polynomials, partially polynomial functions(splines) and Fourier series. Numerical methods for solving linear and nonlinear systems of equations (direct and iterative methods) . Numerical approximation of matrices’eigenvalues and eigenvectors. Numerical integration and differentiation. Methods for solving ordinary and partial differential equations .