Course: Modern Numerical Methods and Algorithms

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Course title Modern Numerical Methods and Algorithms
Course code KMA/PGSA4
Organizational form of instruction Lecture
Level of course Doctoral
Year of study not specified
Semester Winter and summer
Number of ECTS credits 5
Language of instruction Czech, English
Status of course Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Machalová Jitka, doc. RNDr. Ph.D., MBA
Course content
1. Nonsmooth Newton method. 2. Interior point methods. 3. Discontinuous Galerkin method. 4. Direct methods for large sparse systems of linear equations. 5. Iterative methods for large sparse systems of linear equations.

Learning activities and teaching methods
Work with Text (with Book, Textbook)
Learning outcomes
To get an overview about modern numerical methods and algorithms.
Comprehension Understanding of basic modern numerical methods.
Prerequisites
Oral exam: to know and to understand the subject.

Assessment methods and criteria
Oral exam

Oral exam: to know and to understand the subject.
Recommended literature
  • A. George, J. W.-H. Liu. (1981). Computer Solution of Large Sparse Positive Definite Systems. Prentice-Hall, N.J.
  • D. Bertaccini, F. Durastante. (2018). Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications. Chapman and Hall/CRC.
  • Davis, T. A. (2006). Direct Methods for Sparse Linear Systems. SIAM, Philadelphia.
  • Facchinei, F., Pang, J.-S. (2003). Finite-Dimensional Variational Inequalities And Complementarity Problems. Volume I and II. Springer.
  • Hesthaven, J. S., Warburton, T. (2008). Nodal Discontinuous Galerkin Methods. Algorithms, Analysis, and Applications. Springer.
  • Chen, Z. (2005). Finite Element Methods and Their Applications. Springer.
  • Renegar, J. (2001). A Mathematical View of Interior-Point Methods in Convex Optimization. SIAM, Philadelphia.
  • Riviere, B. (2008). Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations: Theory and Implementation. SIAM, Philadelphia.
  • Strang, G. (2007). Computational Science and Engineering. Wellesley-Cambridge Press.
  • Wright, S. J. (1997). Primal-Dual Interior-Point Methods. SIAM, Philadelphia.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Science Study plan (Version): Applied Mathematics (2020) Category: Mathematics courses - Recommended year of study:-, Recommended semester: -