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TANA09 Lectures and Lessons
| Lectures | Description | Chapters |
| F1 Introduction |
Introduction. Basic concepts. Error propagation. Basic arithmetic operations. Catastrophic cancellation. |
1,2.1-2.4 |
| F2 Error analysis |
Floating point systems. Computer arithmetic.
Analysis of computational errors. |
2.5-2.7, 2.8,4.1-4.2 |
| F3 Non-linear equations |
Equation solving. Newton-Raphsons method and the Secant method. Error estimate. Order of convergence. Applications: Ray tracing and implementation of the square root. |
4.1-4.5, 4.7 |
| F4 Linear algebra |
Basic matrix operations. Linear systems. Gaussian elimination and pivoting. The LU and Cholesky decompositions. Vector norms. |
8.1-8.6, 8.10 |
| F5 Approximation |
Matrix norms. Sensitivity for linear systems. The condition number. Least squares problems. The QR decomposition. Circle fitting. |
8.10, 8.12-8.14 |
| F6 Orthogonal matrices |
The singular value decomposition. Fundamental subspaces. Ill-conditioned and rank deficient linear systems. Low rank approximation. Applications: Projections and computer graphics, Data compression, Automatic character recognition. |
8.14 |
| F7 Interpolation |
Polynomials. Newtons formula. Runge's phenomena. Lagrange interpolation. Spline interpolation. |
5.1-5.3, 5.7, 5.8-5.10 |
| F8 Curves |
B-splines. Least squares fits. Parametric curves. Bezier curves. Font design. |
5.10 |
| F9 Extrapolation |
Extrapolation. Integration and differentiation. Adaptive methods. |
6.1-6.4, 7.2. |
The problems are available as a PDF
| Lektion | Uppgifter | Extra |
| L1 | 1.1, 1.2, 1.5, 1.9, 1.10, 2.2, 2.4, 2.8, 2.9 | 1.4, 1.6, 1.7, 1.8, 1.11, 1.14, 2.3, 2.5, 2.6, 2.10 |
| L2 | 3.1, 3.2, 3.4, 3.5, 3.7, 3.12. | 3.3, 3.6, 3.9, 3.10, 3.13. |
| L3 | 7.1, 7.3, 7.5, 7.6, 7.9, 7.12, 7.14, 7.16,
7.17, 7.22, 7.23, 7.25. |
7.2, 7.4, 7.6, 7.10, 7.15, 7.19, 7.20, 7.24, 7.27. |
| L4 | 8.1, 8.4, 8.6, 8.10, 8.15, 8.18, 8.19. | 8.2, 8.3, 8.7, 8.9, 8.16, 8.21. |
| L5 | 4.1, 4.3, 4.5, 4.7, 4.9, 4.11, 4.14, 4.19, 4.20. | 4.2, 4.4, 4.6, 4.8, 4.10, 4.12, 4.16, 4.17, 4.22. |
| L6 | 5.2, 5.4, 5.6, 5.7, 5.11. | 5.1, 5.5, 5.9. |
Sidansvarig: Fredrik Berntsson
Senast uppdaterad: 2023-10-25