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Lecturer(s)
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Machalová Jitka, doc. RNDr. Ph.D., MBA
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Vodák Rostislav, RNDr. Ph.D.
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Course content
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Principles of finite precision computation, sources of errors during computational process, propagation of errors. Number systems based on floating point arithmetic. Multivariate interpolation and approximation. Numerical integration in 2D and 3D. Matrix factorization (LU, Cholesky, Bunch-Parlett, block-partitioned), pseudoinverse matrices, condition numbers, condition number estimation. Conjugate gradient method with preconditioning. Large sparse matrix techniques. Computer implementation accuracy and stability of algorithms. Methods of solution for systems of nonlinear equations (Newton method modifications, quasiNewton 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 a theory and a practical usage of the selected computational methods
Application For the selected numerical methods demonstrate an 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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Golub,G.H., Van Loan C.F. (1996). Matrix computations.. John Hopkins University Press Baltimore.
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Higham, N.J. (1996). Accuracy and stability of numerical algorithms. SIAM, Philadelphia.
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Nocedal, J., Wright, S.J. (1999). Numerical optimization. Springer.
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Segeth, K. (1998). Numerický software I. Karolinum, Praha.
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Stoer, J., Bulirsch, R. (1992). Introduction to numerical analysis.. Springer-Verlag.
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Vitásek, E. (1987). Numerické metody. SNTL, Praha.
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