Fundamentals.

Ch. 0, sections 1, 3, 4, 5.

Solution of nonlinear equations. Bracketing methods. Fixed-point iteration.

Ch. 1, sections 1, 2.

Open methods: Newton-Raphson and its modifications.

Ch. 1, sections 3, 4, 5.

Errors and non-linear equations.

Linear system of equations. Gauss elimination. Operation count. Norms. Ill-conditioning. Swamping.

Chapter 2, sections 2.1, 2.3.

LU factorization. Pivoting.

Chapter 2, sections 2.2, 2.4.

Iterative methods for linear systems. Sparse matrices. Newton's method for several variables.

Chapter 2, sections 2.5, 2.6, 2.7.

Linear equations.

Lecture 7: Lagrange interpolation. Interpolation error. Chapter 3, sections 3.1.1, 3.1.3, 3.1.5, 3.2.1.

Lecture 8: Runge phenomenon. Chebyshev interpolation. Chapter 3, sections 3.2.3, 3.3.1, 3.3.2, 3.3.3.

Lecture 9: Splines. Chapter 3, sections 3.4.1, 3.4.2.

Interpolation.

Bézier curves. Chapter 3, section 3.5.

Least squares. Chapter 4, section 4.1.

Bézier curves and least squares.

QR factorization. Numerical integration. Chapter 4, section 4.3. Chapter 5, sections 5.2, 5.4.

Models for least squares. The Fourier transform. Trigonometric interpolation. Chapter 4, section 4.2. Chapter 10, sections 10.1, 10.2

The FFT and signal processing. Chapter 10, section 10.3

QR factorization, integration, and the Fourier transform.

The Discrete Cosine Transform. Image compression. Chapter 11, sections 11.1, 11.2

Huffman coding. Power iteration methods. Chapter 11, section 11.3. Chapter 12, section 12.1.

Compression

QR algorithm. The Google matrix. Chapter 12, section 12.2.

Singular value decomposition. Chapter 12, sections 12.3, 12.4

Singular value decomposition and applications.

Eigenvalues and singular value decomposition.

Instructor's notes for FMN011, 2012.