470-4506/01 – Selected Chapters on Numerical Methods (VKzNM)
Gurantor department | Department of Applied Mathematics | Credits | 4 |
Subject guarantor | doc. Ing. Dalibor Lukáš, Ph.D. | Subject version guarantor | doc. Ing. Dalibor Lukáš, Ph.D. |
Study level | undergraduate or graduate | Requirement | Optional |
Year | 2 | Semester | summer |
| | Study language | Czech |
Year of introduction | 2015/2016 | Year of cancellation | |
Intended for the faculties | FEI | Intended for study types | Follow-up Master |
Subject aims expressed by acquired skills and competences
The aim of the course is to introduce fundamental numerical methods for solution of engineering problems that lead to large-scale linear systems, nonlinear systems, or eigenvalue problems. Further, we shall present interpolation methods and an approximation by the method of least squares. Finally, we shall focus on numerical derivatives, quadrature, and we introduce methods for solution of boundary value problems for partial diferential equations. Each topic will be motivated by an engineering problem. The algorithms will be implemented in Matlab. The students will be also introduced to some libraries of numerical linear algebra such as BLAS, LAPACK, and MUMPS.
Teaching methods
Lectures
Tutorials
Summary
The course covers fundamental methods of numerical linear and nonlinear algebra, methods of interpolation and approximation, and numerical analysis including an introduction to solution of boundary value problems for partial differential equations.
Compulsory literature:
- Quarteroni, A. – Sacco, R. – Saleri, F. Numerical Mathematics. Springer, 2000.
Recommended literature:
- W.H., Flannery, B.P., Teukolski, S.A., Vetterling, W.T.: Numerical Recipes in C. Cambridge University Press, Cambridge 1990.
Way of continuous check of knowledge in the course of semester
test, project
E-learning
Other requirements
Basic knowledge of linear algebra, derivatives, and integrals
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Lectures:
1. Numerical linear algebra - iterative methods for solution to linear systems
2. Numerical linear algebra - the method of conjugate gradients, preconditioning
3. Numerical linear algebra - sparse matrix solvers, parallel frontal method
4. Numerical linear algebra - eigenvalues and eigenvectors, power method, Lanczos method
5. Numerical linear algebra - libraries BLAS, LAPACK, MUMPS
6. Nonlinear systems - bisection, fixed-point iterations, Newton's method
7. Interpolation and approximation - Lagrange interpolation, splines, B-splines, approximation by the method of least squares
8. Numerical analysis - numerical derivative, numerical quadrature
9. Numerical analysis - introduction to numerics for partial differential equations
10. Numerical analysis - principle of the finite element method
Exercises:
1. Numerical linear algebra - iterative methods for solution to linear systems
2. Numerical linear algebra - the method of conjugate gradients, preconditioning
3. Numerical linear algebra - sparse matrix solvers, parallel frontal method
4. Numerical linear algebra - eigenvalues and eigenvectors, power method, Lanczos method
5. Numerical linear algebra - libraries BLAS, LAPACK, MUMPS
6. Nonlinear systems - bisection, fixed-point iterations, Newton's method
7. Interpolation and approximation - Lagrange interpolation, splines, B-splines, approximation by the method of least squares
8. Numerical analysis - numerical derivative, numerical quadrature
9. Numerical analysis - introduction to numerics for partial differential equations
10. Numerical analysis - principle of the finite element method
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction