Numerical Linear Algebra for Signal Processing
Lecturer: Michael Joham with Hela Jedda
Target Audience: Master EI and MSCE
Language: English
Next Exam: tbd. (no responsibility is taken for the correctness of this information)
Lectures/Tutorials in Summer Semester 2018
Content
Introduction to the fundamentals of numerical linear algebra with the application to signal processing problems. Floating-point arithmetics: IEEE standard, error of floating-point arithmetic. Preliminaries from linear algebra: singular value decomposition (SVD), projectors, matrix norms, Householder reflection, Givens rotation. QR factorization: Gram-Schmidt orthogonalization, Householder triangularization, applications of QR factorization. Back substitution: solving a triangular equation system, inversion of a triangular matrix and application to channel equalization. Least squares: least squares with Cholesky factorization, QR factorization, and SVD; rank-deficient least squares, application to least squares estimation. Condition of a problem: norm-wise & component-wise condition numbers, condition number of basic operations, condition of inner product, matrix-vector product, unitary matrix, and equation system. Stability of an algorithm: backward stability, accuracy based on backward stability; stability of floating-point arithmetic, algebraic operations, Householder triangularization, back substitution; stability of solving equation systems via Householder triangularization. Systems of equations: Gaussian elimination, pivoting, stability of Gaussian elimination; Cholesky factorization, pivoting, stability. Eigenvalues: Hessenberg form; Rayleigh quotient iteration, QR algorithm, application to principal component analysis; SVD, bi-diagonal form, implicit Q-theorem, Golub-Reinsch SVD, application to blind channel estimation. |