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FI:PA081 Numerical Computations - Course Information

## PA081 Programming Numerical Computations

**Faculty of Informatics**

Spring 2020

**Extent and Intensity**- 2/0. 2 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
**Teacher(s)**- Mgr. Aleš Křenek, Ph.D. (lecturer)
**Guaranteed by**- Mgr. Aleš Křenek, Ph.D.

Department of Machine Learning and Data Processing - Faculty of Informatics

Supplier department: Department of Machine Learning and Data Processing - Faculty of Informatics **Prerequisites**- Prerequisites: knowledge of one-dimensional calculus, linear algebra, programming in C and elements of object-oriented programming.
**Course Enrolment Limitations**- The course is also offered to the students of the fields other than those the course is directly associated with.
**Fields of study the course is directly associated with**- there are 49 fields of study the course is directly associated with, display
**Course objectives**- This course is devoted to mathematical and programming techniques needed for exact solution of numerical problems.
**Learning outcomes**- Student will understand basic methods used for solving numerical problems and will be able to suggest and validate methods to be used for solving a particular numerical computing problem.
**Syllabus**- Representation of floating-point numbers. Rounding errors of elementary operations. Accuracy and stability of numerical computations.
- Solution of nonlinear equations. Optimization of functions in one and more dimensions. Numerical integration.
- Eigenvalues and eigenvectors.
- Practical solution of linear algebra problems. Stability of the solution of the least squares problem.
- Automated differentiation.
- Numerical simulation of dynamic behaviour of physical systems.

**Literature**- ACTON, Forman S.
*REAL Computing made real :preventing errors in scientific and engineering calculations*. Princeton: Princeton University Press, 1996. XV, 259 s. ISBN 0-691-03663-2. info - HIGHAM, Nicholas J.
*Accuracy and stability of numerical algorithms*. Philadelphia: Society for Industrial and Applied Mathematics, 1996. xxviii, 68. ISBN 0-89871-355-2. info - STROUSTRUP, Bjarne.
*The C++ programming language*. 3rd ed. Reading: Addison-Wesley, 1997. x, 910 s. ISBN 0-201-88954-4. info - PRESS, William H.
*Numerical recipes in C/C++ the art of scientific computing*. Cambridge: Cambridge University Press, 2002. 1 CD-ROM. ISBN 0521750377. info - GRIEWANK, Andreas and Andrea WALTHER.
*Evaluating derivatives : principles and techniques of algorithmic differentiation*. 2nd ed. Philadelphia: Society for Industrial and Applied Mathematics, 2008. xxi, 438. ISBN 9780898716597. info - SCHNEIDER, Johannes J. and Scott KIRKPATRICK.
*Stochastic optimization*. Berlin: Springer, 2006. xvi, 565. ISBN 3540345590. info

*recommended literature*- ACTON, Forman S.
**Teaching methods**- The course consists of lectures where its topics are presented and discussed in both general level and using specific examples, including comments on program code. The lectures are complemented with optional homeworks and discussion of their solutions during the following lectures.
**Assessment methods**- Final written test, consisting of approx. 10 tasks covering both the theoretical part and practical examples (e.g. design pseudocode to solve a specified problem). The test serves as an extended preparation for the oral exam, where the written answers can be augmented and further points gained. 40% points are required to pass the exam. Results of the optional homework are considered when necessary.
**Language of instruction**- Czech
**Further Comments**- The course is taught annually.

The course is taught: every week.

- Enrolment Statistics (recent)

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