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1. Video lectures given by Prof Gilbert Strang at MIT exits and may
be viewed for free.
These video lectures offer an independent review of the whole subject based
on the textbook in item 1) above.
http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/
2. I suggests that You visit the web-site (for e.g. downloading parts of
the text in the book):
http://math.mit.edu/linearalgebra/
3. On the Top 10 algorithms in the 2000 century.
Introduction: In order to illustrate the importance of some of the
methods for Matrix Computations described in the syllabus we here
include some papers on this issue for download. In particular a review of
the Top 10 algorithms in the 2000 century. One of the methods on this top 10
list where published in 1950 by Magnus
Hestenes, Eduard Stiefel, and Cornelius Lanczos, and remark that Magnus
Hestens was Norwegian. Se the historical overview
Top 10 algorithms . Below you will find the review papers for
download and interestingly at least 3 of the top 10 algorithms are described
in the textbook by Strang, e.g
1) The QR method. 2) And interestingly, the Decompositional Approach to
matrix Composition in linear algebra have revolutionized matrix computations,
and this paper notice the importance of methods like
LU decomposition, QR decomposition, eigenvalue and Schur decomposition,
Cholesky decomposition,
and the Singular Value Decomposition, all topics in the syllabus,
notice the following papers:
- Top 10 algorithms by Editors
Dongarra and Sullivan. (Interestingly the QR algorithm, The
decompositional approach to matrix computations and the Krylov subspace
iteration methods, are 3 of the top 10 algorithms in the 2000 century
competition.)
- The decompositional approach
to Matrix Computations. By G. W. Stewart (2000).
- The QR algorithm by Parlett
(2000). (Describing the amazing QR algorithm for calculationg
eigenvalues)
- Krylov Subspace Iteration by Van der
Horst (2000). (Describes methods who solve large scale linear systems,
Ax=b, by iterative methods and leads to the Conjugate Gradient Method (CGM).)
- Se also links between the CGM, Krylov (controllability) matrices and
the Partial Least Squares (PLS) method used in chemometrics in
Automatica paper DiRuscio2000.
A link to the other papers in the Top 10 list of algorithms, e.g. the
FORTRAN compiler is given in the link,
papers,
FORTRAN compiler
Teacher: Dr. ing., 1. amanuensis David Di Ruscio
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