Course Details

# Numerical methods I

Academic Year 2023/24

DA61 course is part of 12 study plans

D-P-C-SI (N) / PST Summer Semester 1st year

D-P-C-SI (N) / FMI Summer Semester 1st year

D-P-C-SI (N) / KDS Summer Semester 1st year

D-P-C-SI (N) / MGS Summer Semester 1st year

D-P-C-SI (N) / VHS Summer Semester 1st year

D-K-C-SI (N) / VHS Summer Semester 1st year

D-K-C-SI (N) / MGS Summer Semester 1st year

D-K-C-SI (N) / PST Summer Semester 1st year

D-K-C-SI (N) / FMI Summer Semester 1st year

D-K-C-SI (N) / KDS Summer Semester 1st year

D-K-C-GK / GAK Summer Semester 1st year

D-K-E-SI (N) / PST Summer Semester 1st year

Iterative methods. The Banach fixed-point theorem.

Iterative methods for the systems of linear and nonlinear equations.

Direct methods for the systems of linear algebraic equations, matrix inversion, eigenvalues and eigenvectors of matrices.

Interpolation and approximation of functions. Splines.

Numeric differentiation and integration. Extrapolation to the limit.

Course Guarantor

Institute

Objective

Syllabus

2. Basic principles of iterative methods. The Banach fixed-point theorem.

3. Norms of vectors and of matrices, eigenvalues and eigenvectors of matrices. Iterative methods for systems of linear algebraic equations– part I.

4. Iterative methods for linear algebraic equations– part II. Iterative methods for systems of nonlinear equations.

5. Direct methods for systems of linear algebraic equations, LU-decomposition. Systems of linear algebraic equations with special matrice – part I.

6. Systems of linear algebraic equations with special matrices – part II. The methods based on the minimization of a quadratic form.

7. Computing inverse matrices and determinants, the stability and the condition number of a matrix.

8. Eigenvalues of matrices - the power method. Basic principles of interpolation.

9. Polynomial interpolation.

10. Interpolation by means of splines. Orthogonal polynoms.

11. Approximation by the discrete least squares.

12. Numerical differentiation, Richardson´s extrapolation. Numerical integration of functions in one variables– part I.

13. Numerical integration of functions in one variables– part II. Numerical integration of functions in two variables.

Prerequisites

Language of instruction

Czech

Credits

4 credits

Semester

Forms and criteria of assessment

Specification of controlled instruction, the form of instruction, and the form of compensation of the absences

Offered to foreign students

Course on BUT site

Lecture

13 weeks, 3 hours/week, elective

Syllabus