## 2016/17, winter semester: Basics of numerical mathematics: matrix methods Základy numerické matematiky: maticové metody

Charles University, Prague.

Literature: 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. [pdf]