Exercises in Numerical Linear Algebra and Matrix Factorizations

Tom Lyche is professor emeritus at the University of Oslo. His research interests are in numerical analysis, and splines in approximation theory. He is the author with Jean-Louis Merrien of the book "Exercises in Computational Mathematics with MATLAB" and  editor on numerous books on spline methods,  computer aided geometric design and  approximation theory. He has been a co-organizer of many conferences, in particular the  two conference series "Mathematical Methods for Curves and Surfaces" in Norway and "Curves and Surfaces" in France.Georg Muntingh is a research scientist at the Department of Mathematics and Cybernetics at SINTEF Digital. Jointly with Dr. Tor Dokken, he edited the book “SAGA --- Advances in Shapes, Geometry, and Algebra”, published by Springer in 2014. His research has an interdisciplinary nature and spans a wide range of research fields, with papers published on algebraic geometry, approximation theory, combinatorics, geometric modelling, physics and machine learning.Øyvind Ryan is associate professor at the Department of Mathematics at the University of Oslo. His main interest lies in book projects on topics building heavily on linear algebra, and he has published the book “Linear Algebra, Signal Processing, and Wavelets – A Unified Approach”, published by Springer in 2019.

• A Short Review of Linear Algebra.- Diagonally Dominant Tridiagonal Matrices; Three Examples.- Gaussian Eliminationa nd LU Factorizations.- LDL* Factorization and Positive Definite Matrices.- Orthonormal and Unitary Transformations.- Eigenpairs and Similarity Transformations.- The Singular Value Decomposition.- Matrix  Norms and Perturbation Theory for Linear Systems.- Least Squares.- The Kronecker Product .- Fast Direct Solution of a Large Linear System.- The Classical Iterative Methods.- The Conjugate Gradient Method.- Numerical Eigenvalue Problems.- The QR Algorithm.

“This is a companion volume to Lyche’s textbook … on numerical linear algebra and matrix factorization. … This combination of this book of exercises and solutions with the original book makes the text more approachable, and the additional teaching present in the solutions is quite valuable. … This book … would also be useful to instructors teaching a linear algebra course at a comparable level. There are a lot of good exercises here that would supplement those in other texts.” (Bill Satzer, MAA Reviews, July 5, 2021)