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Course, academic year 2018/2019
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Introduction to Numerical Mathematics - NMNM211
Title in English: Úvod do numerické matematiky
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: winter
E-Credits: 8
Hours per week, examination: winter s.:4/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: prof. RNDr. Vladimír Janovský, DrSc.
Class: M Bc. FM
M Bc. FM > Povinné
M Bc. FM > 2. ročník
Classification: Mathematics > Numerical Analysis
Pre-requisite : {At least one 1st year Calculus course}
Incompatibility : NNUM009
Interchangeability : NNUM009
Annotation -
Last update: G_M (16.05.2012)
The first course of numerical analysis for students of Financial Mathematics.
Aim of the course -
Last update: G_M (27.04.2012)

a review of basic computational tools, practical excersises

Course completion requirements - Czech
Last update: prof. RNDr. Vladimír Janovský, DrSc. (22.02.2019)

Podmínkou zápočtu je účast na cvičení and test u počítače. Povaha kontroly studia předmetu vylučuje opakovaní této kontroly.

Literature - Czech
Last update: prof. RNDr. Vladimír Janovský, DrSc. (22.02.2019)

Deuflhard P. and Hohmann A.: Introduction to Scientific Computing, 2nd edition, Springer, 2002

Quarteroni A., Sacco R. and Saleri F.: Numerical mathematics, Springer, 2000

Tebbens J., Hnětýnková I., Plešinger M., Strakoš Z. and Tichý P.: Analýza metod pro maticové výpočty. Základní metody. Matfyz press, Praha, 2012

Teaching methods -
Last update: G_M (27.04.2012)

The course consists of lectures in a lecture hall and exercises in a computer laboratory.

Requirements to the exam -
Last update: G_M (27.04.2012)

Examination according to the syllabus.

Syllabus -
Last update: G_M (27.04.2012)

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.

Entry requirements -
Last update: prof. RNDr. Vladimír Janovský, DrSc. (22.02.2019)

basic knowledge of calculus and linear algebra

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