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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.
Non-linear equations. Existance. Fixed point iteration.

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, 1.7, 2.2, 2.4 1.4, 1.6, 1.8, 2.3, 2.5, 2.6
L2 3.1, 3.2, 3.4, 3.5, 3.7, 3.9 3.3, 3,6, 3.10
L3 4.1,4.4,4.6,4.12,4.15,4.17,4.18,
4.21,4.22,4.24.
4.2,4.5,4.9,4.14,4.16,4.19,4.23,
4.28.
L4 5.1,5.4,5.6,5.10,5.15,5.18,5.19 5.2,5.3,5.7,5.9,5.16,5.21
L5 6.1, 6.3, 6.6, 6.9, 6.12, 6.14, 6.17, 6.19 6.2, 6.4, 6.7, 6.8, 6.10, 6.13, 6.16, 6.18
L6 7.2, 7.3,7.5,7.6 7.1, 7.4,

Sidansvarig: Fredrik Berntsson
Senast uppdaterad: 2019-11-29