Matrix Analysis, CAAM 335, Spring 2012

Supplemental Notes for CAAM 335 Matrix Analysis

These supplemental notes for the course CAAM 335 Matrix Analysis are, as the name suggests, meant to be used in combination with the lectures and with the CAAM 335 course notes. They contain write-ups of some of the material discussed in class as well as several additional examples. You get the most out of these notes if you look through the relevant sections before each class (to recognize wha...

CAAM 453 Numerical Analysis I Rice University

CAAM 454/554: Afternotes on Krylov-Subspace Iterative Methods

These notes are written as supplements to the textbook, “Numerical Linear Algebra” by Lloyd Trefethen and David Bau, for CAAM 454/554 students. Those who are preparing for the CAAM Ph.D Qualifying exam on Numerical Analysis should do the exercises provided in these notes. We will mostly follow the notation of the book. For instance, unless otherwise specified, the norm ‖ · ‖ refers to the Eucli...

Jim Lambers CME 335 Spring Quarter 2010 - 11

One of the major drawbacks of the symmetric QR algorithm is that it is not parallelizable. Each orthogonal similarity transformation that is needed to reduce the original matrix A to diagonal form is dependent upon the previous one. In view of the evolution of parallel architectures, it is therefore worthwhile to consider whether there are alternative approaches to reducing an n × n symmetric m...

The ratios between the spectral norm, the numerical radius and the spectral radius

Recently, Uhlig [Numer. Algorithms, 52(3):335-353, 2009] proposed open questions about the ratios between the spectral norm, the numerical radius and the spectral radius of a square matrix. In this note, we provide some observations to answer these questions. Keywords—Spectral norm, Numerical radius, Spectral radius, Ratios