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The first course of numerical analysis for bachelor study of mathematics. Topics: systems of linear equations, least squares, nonlinear systems, function minimalization, interpolation, ordinary differential equations, eigenvalue problems.
Last update: T_KNM (19.05.2008)
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a review of basic computational tools, practical excersises Last update: JANOVSKY/MFF.CUNI.CZ (30.04.2008)
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Segethová J.: Základy numerické matematiky, MFF UK, 2002 Deuflhard P. and Hohmann A.: Introduction to Scientific Computing, 2nd edition, Springer, 2002 Last update: JANOVSKY (20.04.2006)
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The course consists of lectures in a lecture hall and exercises in a computer laboratory. Last update: T_KNM (19.05.2008)
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Examination according to the syllabus. Last update: T_KNM (19.05.2008)
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Solving liner systems, direct methods: Gauss elimination, LU-decomposition, pivoting, Cholesky decompositon.
Least Squares: data fitting, linear least squares, normal equation, pseudoinverse, QR-decomposition.
Nonlinear systems: Fixed Point Theorem (contraction mapping), Newton's Method, Newton-like methods.
Function minimization: Nelder-Mead Method, Method of Steepest Descent, Conjugate Gradient Method.
Interpolation: Lagrange Interpolating Polynomial, Chebyshev Polynomial, splines.
Ordinary Differential Equations: initial value problem, Euler Method, implicit Euler Method, Runge-Kutta Method.
Eigenvalue problems: a primer (eigenvalue, eigenvector, Characteristic Polynomial, multiplicity, Similar Matrices, Jordan canonical form), Power Method, Inverse iteration, QR algoritmus.
Iterative Methods (linear systems): large sparse matrices, Gauss-Seidel Method, Successive Overrelaxation Method, Conjugate Gradient Method, preconditioning. Last update: T_KNM (19.05.2008)
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basic knowledge of calculus and linear algebra Last update: T_KNM (19.05.2008)
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