2016/17, winter semester:
Basics of numerical mathematics: matrix methods
Charles University, Prague.
Základy numerické matematiky: maticové metody
J.D. Tebbens, I. Hnetynkova, M. Plesinger, Z. Strakos, P. Tichy:
Analysis of Methods for Matrix Computations, Matfyzpress, Praha, 2012 (in Czech).
The lecture covers chapters 1--7 of the book (without extended parts of these chapters,
an exception is the
part devoted to the Arnoldi algorithm). More details below.
The exam will test the general knowledge and understanding to the basic concepts
of numerical matrix computations. Questions in the written exam will be rather general.
Based on the results, the student will pass. The oral exam can be on demand (from both
the side of the lecturer and student). The exam will cover, in particular, the following parts
of the above mentioned book:
Chapter 1: 1.1 -- 1.7 (Preliminaries)
Chapter 2: 2.1 -- 2.2 (Schur theorem and its consequences)
Chapter 3: 3.1 -- 3.5 (Orthogonal transformations and QR factorization) + 3.6 (Arnoldi algorithm)
Chapter 4: 4.1 -- 4.4 + 4.6 (Theorem 4.9 without the proof) + 4.7 (Iteration refinement) + 4.10
Chapter 5: 5.1 + 5.2 (without 5.2.3) + 5.3.1 + 5.3.2
Chapter 6: 6.1 -- 6.3 (Linear least squares)
Chapter 7: until Lemma 7.2 (Arnoldi method, Lanczos method, theoretical and practical differences)
+ Power method from lectures (idea, the presented theorem, the proof)
Additional text that contains: floating-point arithmetics (first lecture), solving nonlinear
equations and systems (lecture 13.12.2016 and 14.12.2016), comments on simple iterative methods
for solving systems of linear equations (lecture 14.12.2016). Exam may contain only those parts that
were actually presented.