Sz 12:15-14:00 (H607)
Cs 12:15-14:00 (KF86)
News
- All points have been uploaded to the Neptun system. The midterm marks will be calculated from these points, and will be uploded to Neptun within a few days.
- The continuation of the Numerical methods course (in Hungarian): Numerikus módszerek 2 - parciális differenciálegyenletek - A tervek szerint az előadás ideje K16, a laborgyakorlaté pedig CS14. A kurzus csak kétévente indul. A következő alkalom: 2018/19. II. félév. A két évvel ezelőtti kurzus honlapja alapján látható a tárgy tematikája és a követelményrendszer. new!
- Matlab news (some parts in Hungarian)
- MSc thesis topics (in Hungarian)
- Webpage of the Miklós Farkas Seminar on Applied Analysis - Thursdays from 10:15, the talks are in English on regular basis
- BME has a TAH Matlab licence. Thus, Matlab is available for all students and teachers. The installation guide can be found at this inner link (in Hungarian).
Auxilary material for the course
- Slides of the lectures: part I (Numerical linear algebra - printer friendly version)
- Slides of the lectures: part II (Nonlinear equations, interpolation - printer friendly version)
- Slides of the lectures: part III (Numerical differentiation and integration - printer friendly version)
- Slides of the lectures: part IV (One-step methods for initial value problems - printer friendly version)
- Slides of the lectures: part V (last part) (Predictor-corrector methods, multistep methods, solution of boundary value problems - printer friendly version)
- The electronic lecture notes to the course in Hungarian: Faragó István-Horváth Róbert, Numerikus módszerek, BME 2013.
- The error reporting form to the lecture notes. (List of errors so far) Plese report here the errors you have found (in Hungarian).
- Problem book in Hungarian: Faragó István - Fekete Imre - Horváth Róbert: Numerikus módszerek példatár, 2013.
- The error reporting form to the problem book. (List of errors so far) Plese report here the errors you have found (in Hungarian).
- Numerical computing with Matlab (lecture notes from Matlab with the NCM toolbox)
- Using Matlab - The language of technical computing (Matlab user guide)
- Two-hour introductory tutorial to Matlab
The schedule of the lectures and computer labs:
| Week | Lecture (We12, Th12) | Computer lab (We14 and Th14) |
|---|---|---|
| 1. 03/09 |
Wednesday: The requirements of the course. The topics of the course. Model construction and its necessity. Properly posed problems. Conditioning of a problem and of a computation. Error sources of a model. Thursday: Vector and matrix norms, spectral radius, relation between norms and eigenvalues, convergence speed of sequences |
Special matrices. Matrix and vector norms. |
| 2. 10/09 |
Wednesday: Floating point numbers and their properties Conrad Zuse - Computer history (video) Thursday: Conditioning of SLAEs, condition numbers of matrices, Gaussian method and its investigation. |
Norms and eigenvalues, order of convergence. Problems - week 2 (with homework assignments) - Matlab m-file - week 2 |
| 3. 17/09 |
Wednesday: LU decomposition. Performance of the Gaussian method. Pivoting. General LU decomposition. Thursday: University Sports Day - there are no lessons |
Condition numbers and conditioning. Floating point numbers. Conditioning of linear systems. Gaussian method, LU decomposition. Problems - weeks 3-4 (with homework assignments) - Matlab m-file - weeks 3-4 Due to the University Sports Day, the computer lab on Thursday is cancelled. |
| 4. 24/09 |
Wednesday: Dean's day - there are no lessons at the Faculty of Natural Sciences Thursday: $LDM^T$ decomposition, Cholesky decomposition. The left division command of Matlab. Iteration methods for SLAEs. Necessary and sufficient condition for the convergence. Error estimation with the Banach fixed point theorem. Jacobi and Gauss-Seidel methods. |
Condition numbers and conditioning. Floating point numbers. Conditioning of linear systems. Gaussian method, LU decomposition. Problems - weeks 3-4 (with homework assignments) - Matlab m-file - weeks 3-4 Due to the Dean's Day, the computer lab on Wednesday is cancelled. |
|
5. 01/10 |
Wednesday: Relaxation mehods. Conditions for the convergence. Introduction to the conjugate gradient method. Thursday: The conjugate gradient method. |
Partial pivoting, general LU decomposition, Cholesky decomposition, Classical iterative methods of linear systems. Problems - week 5 (with homework assignments) - Matlab m-file - week 5 |
| 6. 08/10 |
Wednesday: Householder reflection, Givens rotation, QR decomposition. Thursday: Solution of over-determined systems. Eigenvalue problems: QR iteration for eigenvalue problems. Saturday: Eigenvalue problems: the power method and its different versions. This is an extra work day, which replaces a Monday (22 October). However, the teaching is organized according to the Thursday's schedule at BME. |
Gradient methods, $QR$ decomposition with Householder reflections and Givens rotations. Over-determined systems. Problems - week 6 (with homework assignments) - Matlab m-file - week 6 Thursday's group has an extra computer lab on Saturday! |
|
7. 15/10 |
Wednesday: Conditioning of eigenvalue problems. Solution of nonlinear equations: Localization of roots. Bisection method. Conditioning. Thursday: Solution of nonlinear equations: Newton's method, fixed point iterations. |
Eigenvalue problems Problems - week 7 (with homework assignments) - Matlab m-file - week 7 |
| 8. 22/10 | Wednesday: Solution of nonlinear systems, unconstrained numerical optimization. interpolation with polynomials. Lagrange interpolation. Thursday: Test I (Topic: from the beginning of the semester to the over-determined systems. Students are allowed to use one side of an A4 sheet with handwritten reminders, pens and calculator.) |
Nonlinear equations Problems - week 8 (with homework assignments) - Matlab m-file - week 8 |
| 9. 29/10 | Wednesday: Interpolation error. Interpolation on Chebyshev nodes. Thursday: All saints' day - there are no lessons. |
No new problem sheet Due to the All saints' day, the computer lab on Thursday is cancelled. |
|
10. 05/11 |
Wednesday: Newton interpolation. Conditioning of interpolation. Hermite and spline interpolation. Thursday: Trigonometric interpolation. |
Interpolation problems Problems - week 10 (with homework assignments) - Matlab m-file - week 10 |
| 11. 12/11 | Wednesday: Scientific conference of students - there are no lessons. Thursday: Fast Fourier transform. |
Trigonometric interpolation, numerical differentiation Problems - week 11 (with homework assignments) - Matlab m-file - week 11 Due to the scientific conference of students the computer lab on Wednesday is cancelled. |
| 12. 19/11 | Wednesday: Numerical differentiation. Numerical integration with Newton-Cotes formulas. Thursday: Gauss quadrature. |
Numerical integration, numerical solution of initial and boundary value problems Problems - weeks 12-14 (with homework assignments - the last problem sheet of the semester) - Matlab m-file - weeks 12-14 |
| 13. 26/11 | Wednesday: Introduction to the numerical solution of initial value problems. Thursday: Absolute stability, stiffness. | No new problem sheet. |
| 14. 03/12 | Wednesday: Multistep methods. Boundary value problems. Thursday: Test II (Topic: from the solution of eigenvalue problems to the end of the semester. Students are allowed to use one side of an A4 sheet (the other side of the previous crib sheet) with handwritten reminders, pens and calculator.) | No new problem sheet. |
Previous midterm tests with solutions (mostly in Hungarian)
- midterm test II, 2018/19 autumn -- Solutions
- midterm test I, 2018/19 autumn -- Solutions
- II. zárthelyi dolgozat, 17/18/I. félév (English translation of the midterm test II) -- Megoldások (English translations of the solutions)
- I. zárthelyi dolgozat, 17/18/I. félév (English translation of the midterm test I) -- Megoldások (English translations of the solutions)
- röpdolgozat minta, 17/18/I. félév (feladatok és megoldások)
- II. zárthelyi dolgozat, 16/17/I. félév -- Megoldások
- I. zárthelyi dolgozat, 16/17/I. félév -- Megoldások
- II. zárthelyi dolgozat, 15/16/I. félév -- Megoldások
- I. zárthelyi dolgozat, 15/16/I. félév -- Megoldások
- II. zárthelyi dolgozat, 14/15/I. félév -- Megoldások
- I. zárthelyi dolgozat, 14/15/I. félév -- Megoldások
- II. zárthelyi dolgozat, 13/14/I. félév -- Megoldások
- I. zárthelyi dolgozat, 13/14/I. félév -- Megoldások
- II. zárthelyi dolgozat, 12/13/I. félév -- Megoldások
- I. zárthelyi dolgozat, 12/13/I. félév -- Megoldások
- II. zárthelyi dolgozat, 11/12/I. félév -- Megoldások
- I. zárthelyi pótdolgozat, 11/12/I. félév -- Megoldások
- I. zárthelyi dolgozat, 11/12/I. félév -- Megoldások
- II. zárthelyi dolgozat, 10/11/I. félév -- Megoldások
- I. zárthelyi pótdolgozat, 10/11/I. félév -- Megoldások
- I. zárthelyi dolgozat, 10/11/I. félév -- Megoldások
- II. zárthelyi dolgozat, 09/10/I. félév -- Megoldások
- I. zárthelyi pótdolgozat, 09/10/I. félév -- Megoldások
- I. zárthelyi dolgozat, 09/10/I. félév -- Megoldások
- II. zárthelyi pótdolgozat, 08/09/I. félév -- Megoldások
- II. zárthelyi dolgozat, 08/09/I. félév -- Megoldások
- Mintazárthelyi, 08/09/I. félév, II.zh
- I. zárthelyi pótdolgozat, 08/09/I. félév -- Megoldások
- I. zárthelyi dolgozat, 08/09/I. félév -- Megoldások
- Mintazárthelyi, 08/09/I. félév, I.zh
Useful links
- MATLAB website
- The free Matlab clone Addi that is written for android. The extension to draw graphs.
- Stoyan G., Takó G., Numerikus módszerek I. / Numerical methods book (in Hungarian).
- A BSc thesis written by Gergely Csomós about Runge's example (in Hungarian)
- Page on disasters due to numerical errors
- George E. Forsythe: Pitfalls in Computation, or why a Math Book isn't Enough
- A paper about the further acceleration of FFT
- Pictures of numerical linear algebra conference from 1977 with a number of researchers mentioned in the lectures (Thanks to Miklós Antal Werner.)
- The paper of Erdős and Turán about the estimation of Lebesgue's constant
- The MacTutor History of Mathematics archive