Numeric Methods

Lecturer:

Petr Kubera (gar.)

Tutor:

Petr Kubera (gar.)

Supervisor:

Synopsis:

The aim of this course is to provide students with a basic knowledge of numerical methods.

Requirements:

Syllabus of lectures:

Introduction to numerical mathematics: round off errors, stability of algorithms, problem conditioning

Function interpolation: Lagrange interpolation polynomial, Newton interpolation polynomial, A-N scheme, spline

Function approximation: least squares method

Numerical derivation and quadrature: forward, backward and central schemes, Newton-Cotes quadrature, Gauss quadrature, composite rules, Romberg algorithm

Solution of nonlinear equations and system of nonlinear equations

Polynomial root finding: Laguerre algorithm, Bernoulli algorithm

System of linear equations-directs method: GEM, Gauss-Jordan algorithm, LU decomposition, Cholesky decomposition, QR decomposition.

Iterative methods for system of linear equation: Richardson method, Jacobi method, Gauss-Seidel method, SOR, gradient methods-introduction

Eigenvalue finding : power method, Rayleigh method

Introduction to numerical solution of ordinary differential equation: Cauchy problem, Runge-Kutta method, multi-steps methods

Syllabus of tutorials:

The structure of exercises is identical to lectures. Exercises are focused on typical problems from each theme.

Introduction to numerical mathematics: round off errors, stability of algorithms, problem conditioning

Function interpolation: Lagrange interpolation polynomial, Newton interpolation polynomial, A-N scheme, spline

Function approximation: least squares method

Numerical derivation and quadrature: forward, backward and central schemes, Newton-Cotes quadrature, Gauss quadrature, composite rules, Romberg algorithm

Solution of nonlinear equations and system of nonlinear equations

Polynomial root finding: Laguerre algorithm, Bernoulli algorithm

System of linear equations-directs method: GEM, Gauss-Jordan algorithm, LU decomposition, Cholesky decomposition, QR decomposition.

Iterative methods for system of linear equation: Richardson method, Jacobi method, Gauss-Seidel method, SOR, gradient methods-introduction

Eigenvalue finding : power method, Rayleigh method

Introduction to numerical solution of ordinary differential equation: Cauchy problem, Runge-Kutta method, multi-steps methods

Study Objective:

Knowledge: The aim of this course is to provide students basic overview of methods numerical mathematics.

Abilities: Students gains ability to select and use appropriate method for each type of problem.

Study materials:

Key references:

Introduction to numerical mathematics; Jitka Segethová; Univerzita Karlova; 2002 Praha; „in Czech“

Numerical methods; Emil Vitásek; Státní nakladatelství technické literatury; 1987 Praha; „in Czech“

Recommended references:

Introduction to numerical mathematics; Anthony Ralston; Academia; 1978 Praha, „in Czech“

Numerical Mathematics; Alfio Quarteroni, Riccardo Sacco, Fausto Saleri; Springer 2000

Media and tools:

calculator, computer

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans: