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Lecturer(s)
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Vodák Rostislav, RNDr. Ph.D.
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Machalová Jitka, doc. RNDr. Ph.D., MBA
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Course content
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Interior-point methods. The logarithmic barrier approach. The primal-dual methods. Application to linear programming. Solution of the linear complementarity problem. Convex quadratic programming solution using interior-point methods. Computer realization of interior-point methods. Solution of large sparse systems of equations. Using direct methods: elimination trees, supernodes, block partitioning exploitation, frontal and multifrontal methods. Using iterative methods: preconditioning conjugate gradient method, QMR method, GMRES method, basic ideas of multigrid methods.
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Learning activities and teaching methods
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Dialogic Lecture (Discussion, Dialog, Brainstorming), Work with Text (with Book, Textbook)
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Learning outcomes
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Master selected modern numerical methods and tecnologies.
Application Demonstrate a good orientation in modern numerical methods and ability of their usage.
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Prerequisites
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Master's degree in mathematics.
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Assessment methods and criteria
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Oral exam
Exam: to know and to understand the subject
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Recommended literature
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Duff, I. S., Erisman, A. M., Reid, J. K. (1997). Direct Methods for Sparse Matrices.. Claredon Press, Oxford.
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George, A., Liu, J.W.-H. (1981). Computer Solution of Large Sparse Positive Definite Systems.. Prentice-Hall, N.J.
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Nocedal J., Wright S.J. (1999). Numerical optimization. Springer.
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Roos C., Terlaky T., Vial J.-P. (2005). Interior point methods for linear optimization. Revised edition.. Springer.
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Wolfgang Hackbush. (1995). Iterative Solution of Large Spase Systéme of Equations. Springer-Verlag.
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