Sz 12:15-14:00 (H406)
Cs 12:15-14:00 (H406)
Course requirements
News
- New! I would like to ask students who are going to write one of the tests again to indicate this intent using this webform. The retake tests will be on 19 December (Thursday), 10:00, room H406. Those who are going to retake both tests first write test II from 10:00 and then test I from 14:30 (H27) in the afternoon. Students may view their second test at 9:30-10-30, 17 December (Tuesday), H24b.
- 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) or at the beginning of the Matlab news page (in English).
- Matlab presentation for students about the TAH licence. 19th of September, Thursday 16:00-18:00 - ABC of the MATLAB Campus Wide License, room: K195. Registration at regisztracio.bme.hu. The poster of the presentation is available at the Matlab news page.
- 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
Main material for the course
- Slides of the lectures: printer friendly version
- Problems for the computer labs and an auxiliary Matlab m-file
Auxilary material for the course
- 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. 09/09 |
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: University Sports Day - the lecture is cancelled |
We: Special matrices. Vector norms. (Pr. 1-6, 8) Th: Due to the University Sports Day, the computer lab on Thursday is cancelled. |
| 2. 16/09 |
Wednesday: Vector and matrix norms, spectral radius, relation between norms and eigenvalues, convergence speed of sequences. Thursday: Floating point numbers and their properties Conrad Zuse - Computer history (video) |
We: Matrix norms, norms and eigenvalues, order of convergence, condition numbers, conditioning. (Pr.: 10,11-13,15-17,19-20(a-b) - we skipped Pr. 7,9,14,18 ; these are left to practice at home). Th: Special matrices. Vector and matrix norms. (Pr.: 1-10 - we skipped Pr. 9, this is left to practice at home) |
| 3. 23/09 |
Wednesday: Conditioning of SLAEs, condition numbers of matrices, Gaussian method and its investigation. Thursday: LU decomposition. Performance of the Gaussian method. Pivoting. |
We: Conditioning, foating point numbers, conditioning of linear systems. (Pr.: 20(c-d)-22,24--27,31-33 - we skipped Pr. 23 (discussed in the lecture) and Pr. 28-30 (discussed later)) Th: Matrix norms, norms and eigenvalues, order of convergence. (Pr.: 11-13, 15-17, 19 - we skipped Pr. 14,18; these are left to practice at home) |
| 4. 30/09 |
Wednesday: Dean's day - there are no lessons at the Faculty of Natural Sciences. The lecture is cancelled. Thursday: General LU decomposition. $LDM^T$ 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. |
We: Due to the Dean's Day, the computer lab on Wednesday is cancelled. Th: Condition numbers, conditioning. Floating point numbers. (Pr.: 20-28.)
|
| 5. 07/10 | Wednesday: Classical iterative methods (Jacobi, Gauss-Seidel and their relaxed versions) and their convergence. Thursday: Gradient and conjugate gradient methods. |
We.: Direct methods for linear systems. (Pr.: 28-30, 34-39) Th.: Conditioning of linear systems.Gaussian method, LU-decomposition, partial pivoting. (Pr.: 31-36, we skipped Pr. 29 (a similar problem will be solved later) and 30 (easy)) |
| 6. 14/10 | Wednesday: Householder reflection, QR decomposition. Thursday: Givens rotation and QR decomposition with Givens rotations. Solution of over-determined systems. Conditioning of eigenvalue problems. |
We.: Iterative methods for linear systems. (Pr.: 40-42, Pr. 43-44 is for practice at home, we skip Pr. 45) Th.: Cholesky decomposition. Classical iterative methods. (Pr.: 37-41)
|
| 7. 21/10 | Wednesday: National holiday, 23 October. The lecture is cancelled. Thursday: Eigenvalue problems (power method, inverse iteration, Rayleigh coefficient iteration, rank deflation). |
We.: National holiday, 23 October. The computer lab is cancelled. Th.: Gradient and conjugate gradien method. Householder reflection, Givens rotation, QR decomposition. (Pr.: 42-45, 48, 46(only Householder)) |
| 8. 28/10 | Wednesday: Eigenvalue problems (QR iteration, reduction to Hessenberg form, shifting). Thursday: Test I in the time slot of the lecture but in different location: room R108. The topic is from the beginning of the semester to the conjugate gradient method. See the previous tests below. |
We.: QR decomposition with Householder reflections and Givens rotations, over-determined linear systems (Pr:: 46-51) Th.: QR decomposition with Householder reflections and Givens rotations, over-determined linear systems (Pr.: 46-47, 49-52) |
| 9 4/11 |
Wednesday: Solution of nonlinear equations: Newton's method, fixed point iterations. Thursday: Solution of nonlinear systems, unconstrained numerical optimization. Interpolation with polynomials. Lagrange interpolation. |
We.: Solution of eigenvalue problems (Pr.: 52-56 (as homework)) Th.: Solution of eigenvalue problems (Pr.: 53-56 (as homework)) |
| 10. 11/11 | Wednesday: Interpolation error. Interpolation on Chebyshev nodes. Thursday: Newton interpolation. Hermite and spline interpolation. |
We.: Solution of nonlinear equations (Pr.: 57-58, 60-62 (Pr. 59 is similar to Pr. 57, Pr 62 is homework)) Th.: Solution of nonlinear equations (Pr.: 57-58, 60-62 (Pr. 59 is similar to Pr. 57, Pr 62 is homework)) |
| 11. 18/11 | Wednesday: Trigonometric interpolation. Thursday: Fast Fourier transform. | We.: Polynomial and spline interpolation (Pr.: 63-68.) Homework for week 11 Th.: Polynomial and spline interpolation (Pr.: 63-68.) |
| 12. 25/11 | Wednesday: Numerical differentiation. Numerical integration with Newton-Cotes formulas. Thursday: Motivation of Gaussian quadrature. | We.: Trigonometric interpolation (pianosound.mat), numerical differentiation. (Pr. 69-71). Homework for week 12 (last homework) Th.: Trigonometric interpolation (pianosound.mat), numerical differentiation (Pr. 69-71). |
| 13. 2/12 | Wednesday: Gaussian quadrature. Introduction to the numerical solutions of ordinary differential equations. Thursday: Runge-Kutta methods. Absolute stability, stiffness. | We.: Numerical integration (Pr. 74-77)
Th.: Numerical integration (Pr. 74-77) |
| 14. 9/12 | Wednesday: Multistep methods. Boundary value problems. Thursday: Test II in the time slot of the lecture but in different location: room R108. The topic is from Householder reflections to numerical integration. See the previous tests below. | We.: Solution of ordinary differential equations (Pr. 78-84)
Th.: Solution of ordinary differential equations (Pr. 78-84) |
Previous midterm tests with solutions (mostly in Hungarian)
- midterm test II, 2019/20 autumn -- Solutions
- midterm test I, 2019/20 autumn -- Solutions
- 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
- 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 MacTutor History of Mathematics archive