NumMeth Lc

“Polynomials of high degree
can be quite unkind…”

Numerical methods Lecture (in English)

In this subject we discuss some classical and modern algorithms, notions and aspects of computer calculations for the solution of various mathematical, scientific and engineering problems. It consists of 2 hours lecture and 2 hours practice weekly.

The topics of the semester include floating point calculations, error propagation, solution of linear systems, matrix norms, nonlinear equations, interpolation, least-squares and quadrature.

The pre-requisite is the completion of Analysis II. We rely on calculations with matrices, convergence, differentiation and integral. Also some experience with programming involving floating point numbers is assumed.

Administrative information

Subject:Numerical Methods Lecture
Computer Science BSc (in English)
Code:IP-18fNM1E
Semester:Spring 2023/2024
Teacher:Mr. Lócsi, Levente
Time:Tuesdays between 12:15 and 13:45
Location:South Building, Room 0-804 (Lóczy)

Description – requirements, dates

Following the lectures is compulsory, 3 misses are allowed.

You need to get a passing grade in the practice part, before you want to go for the exam (of the lecture). Without a passing practice grade you may not take the exam (to pass the lecture part too). The exam consist of a written and an oral part.

The detailed requirements and all further material is available in the University's Canvas system, and in Teams.

Lectures – short summary, plan

1. (2024.02.13.) Machine numbers.
2. (2024.02.20.) Error analysis, Solving systems of linear equations.
3. (2024.02.27.) Gaussian elimination, LU decomposition.
4. (2024.03.04.) LU decomposition, vector norms.
5. (2024.03.12.) Matrix norms, sensitivity of linear systems.
6. (2024.03.19.) On polynomials: root estimates, Horner's method.
7. (2024.03.26.) Nonlinear equations I.
(2024.04.02.) Spring break.
8. (2024.04.09.) Nonlinear equations II.
9. (2024.04.16.) Polynomial interpolation I.
10. (2024.04.23.) Polynomial interpolation II.
11. (2024.04.30.) Least squares & Numerical quadrature I.
12. (2024.05.07.) Numerical quadrature II.
13. (2024.05.14.) A glimpse at further numerical methods.

Links

A handful of links related to this course.

Numanal Department of Numerical Analysis
Canvas The ELTE Canvas system
BG, DT, KK, KP Teachers of the Practice groups:
Gergő Bognár, Tamás Dózsa, Kateryna Krén, Péter Kovács