Lecture 9
Conditioning and Stability I
MIT 18.335J / 6.337J
Introduction to Numerical Methods
Per-Olof Persson ([email protected])
October 10, 2007
1
Conditioning
Absolute Condition Number of a differe
Notes on Conditioning
Robert A. van de Geijn
The University of Texas
Austin, TX 78712
October 6, 2014
NOTE: I have not thoroughly proof-read these notes!
1
Motivation
Correctness in the presence of er
Notes on Eigenvalues and Eigenvectors
Robert A. van de Geijn
Department of Computer Science
The University of Texas
Austin, TX 78712
[email protected]
October 31, 2014
If you have forgotten how to nd
Notes on Gram-Schmidt QR Factorization
Robert A. van de Geijn
Department of Computer Science
The University of Texas
Austin, TX 78712
[email protected]
September 15, 2014
A classic problem in linear
Chapter 4
Singular Value
Decomposition
In order to solve linear systems with a general rectangular coecient matrix, we
introduce the singular value decomposition. It is one of the most important tools
Lecture 3 Part I: Norms
Robert A. van de Geijn
The University of Texas at Austin
Numerical Analysis: Linear Algebra Fall 2011
vertiujilogo
http:/z.cs.utexas.edu/wiki/rvdg.wiki/
1
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Notes on Conditioning
Robert A. van de Geijn
The University of Texas
Austin, TX 78712
October 16, 2014
NOTE: I have not thoroughly proof-read these notes!
1
Motivation
Correctness in the presence of e
Notes on Gram-Schmidt QR Factorization
Robert A. van de Geijn
Department of Computer Science
The University of Texas
Austin, TX 78712
[email protected]
October 16, 2014
A classic problem in linear al
Notes on Vector and Matrix Operations
Robert A. van de Geijn
Department of Computer Science
The University of Texas at Austin
Austin, TX 78712
[email protected]
September 2, 2014
1
(Hermitian) Transp
Lecture 8 - Floating Point Arithmetic,
The IEEE Standard
MIT 18.335J / 6.337J
Introduction to Numerical Methods
Per-Olof Persson ([email protected])
October 3, 2007
1
Floating Point Formats
Scientic no
Lecture 3
The Singular Value Decomposition
MIT 18.335J / 6.337J
Introduction to Numerical Methods
Per-Olof Persson ([email protected])
September 12, 2007
1
The SVD - The Main Idea
Motivation:
The image
Lecture 4
The QR Factorization
MIT 18.335J / 6.337J
Introduction to Numerical Methods
Per-Olof Persson ([email protected])
September 17, 2007
1
Projectors
A projector is a square matrix P that satises
Lecture 2
Orthogonal Vectors and Matrices, Norms
MIT 18.335J / 6.337J
Introduction to Numerical Methods
Per-Olof Persson ([email protected])
September 10, 2007
1
Transpose and Adjoint
For real A, the t
Notes on the Singular Value Decomposition
Robert A. van de Geijn
The University of Texas at Austin
Austin, TX 78712
September 18, 2014
NOTE: I have not thoroughly proof-read these notes!
We recommend
Notes on the Singular Value Decomposition
Robert A. van de Geijn
The University of Texas at Austin
Austin, TX 78712
September 11, 2014
NOTE: I have not thoroughly proof-read these notes!
We recommend
Notes on Numerical Stability
Robert A. van de Geijn
The University of Texas
Austin, TX 78712
October 16, 2014
Based on
Goal-Oriented and Modular Stability Analysis [3, 4]
by
Paolo Bientinesi and Rober
Notes on Numerical Stability
Robert A. van de Geijn
The University of Texas
Austin, TX 78712
October 10, 2014
Based on
Goal-Oriented and Modular Stability Analysis [3, 4]
by
Paolo Bientinesi and Rober
Notes on Vector and Matrix Norms
Robert A. van de Geijn
Department of Computer Science
The University of Texas at Austin
Austin, TX 78712
[email protected]
September 11, 2014
1
Absolute Value
Recall
Notes on Vector and Matrix Norms
Robert A. van de Geijn
Department of Computer Science
The University of Texas at Austin
Austin, TX 78712
[email protected]
September 15, 2014
1
Absolute Value
Recall
7
jth column of A
Notice: rjj = norm(aj) NOT 1/norm(ajj).
one explanation: we assumed A is full rank. But
notice that the example above approaches a rank one matrix. So
how does our method behave when