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CPS615 Linear Algebra Presentation

Given by Geoffrey C. Fox at CPS615 Fall Semester 95 Simulation Track on 18 November 95. Foils prepared 8 Nov 1995

This is designed to augment the Fosdick and Jessup online resource called
A Review of Selected Topics from Numerical Analysis
situated at: http://www.cs.colorado.edu/95-96/courses/materials.hpsc.html
We focus on additional discussion of eigenvectors and eigenvalues which are used in CPS615 in discussing convergence of iterative PDE solvers
Also have small discussion of "functional analysis" with differential operators

This mixed presentation uses parts of the following base foilsets which can also be looked at on their own! 
CPS615-Master95          Miscellaneous CPS615 Foils
CPS615Eigs95             CPS615 Foils on  Matrices -- Eigenvalues and 
                          Vectors
CPS615FEMetc95           CPS615 Foils on Finite Element Methods, Gauss
                           Seidel, Conjugate Gradient and Differential
                           Operators

Table of Contents for CPS615 Linear Algebra Presentation

These foils are designed to be used with Fosdick Jessup Overview of Numerical Analysis 
          CPS615-Master95 003 001 CPS615 -- Base Course for the 
                                  Simulation Track of Computational 
                                  Science
                                  Fall Semester 1995 --
                                  Numerical Analysis for Linear 
                                  Algebra
          CPS615-Master95 004 002 Abstract of CPS615 Numerical 
                                  Analysis Presentation
             CPS615Eigs95 001 003 1:Definition of a Matrix
             CPS615Eigs95 002 004 2:The Definition of a Vector
             CPS615Eigs95 003 005 3:The Definition of Scalar Products 
                                   and Orthonormality
             CPS615Eigs95 004 006 4:Types of Matrices
             CPS615Eigs95 005 007 5:Eigenvectors and Eigenvalues
             CPS615Eigs95 006 008 6:Structure of Matrix
             CPS615Eigs95 007 009 7:Equations for Eigenvalues---I
             CPS615Eigs95 008 010 8:Equations for Eigenvalues---II
             CPS615Eigs95 009 011 9:Polynomial Equations for 
                                  Eigenvalues
             CPS615Eigs95 010 012 10:General Properties of Eigenvalues
             CPS615Eigs95 011 013 11:Eigenvalues of Hermitean 
                                  Matrices---I
             CPS615Eigs95 012 014 12:Eigenvalues of Hermitean 
                                  Matrices---II
             CPS615Eigs95 013 015 13:Orthogonality of Eigenvectors  of
                                   Hermitean Matrices
             CPS615Eigs95 014 016 14:Orthonormal Eigenvectors and  
                                  Unitary Transformation Matrices
             CPS615Eigs95 015 017 15:Diagonal Form of General  
                                  Hermitean Matrix---I
             CPS615Eigs95 016 018 16:Diagonal Form of General  
                                  Hermitean Matrix---II
             CPS615Eigs95 017 019 17:Eigenvectors and Eigenvalues of  
                                  Symmetric Matrices
A modest discussion of differential operators as linear operators 
           CPS615FEMetc95 001 020 1:Finite and Infinite Dimensional  
                                  Matrices as Operators
           CPS615FEMetc95 002 021 2:d/dx as an Operator and Its  
                                  Scalar Products
           CPS615FEMetc95 003 022 3:d/dx as a Hermitean Operator
           CPS615FEMetc95 004 023 4:The Laplacian as a (Matrix) 
                                  Operator
           CPS615FEMetc95 005 024 5:Mapping of Function Spaces  to a 
                                  Finite Number of Dimensions

List of Foils Used as they occur 

CPS615-Master95          Miscellaneous CPS615 Foils
3 4 
CPS615Eigs95             CPS615 Foils on  Matrices -- Eigenvalues and 
                          Vectors
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 
CPS615FEMetc95           CPS615 Foils on Finite Element Methods, Gauss
                           Seidel, Conjugate Gradient and Differential
                           Operators
1 2 3 4 5

Sorted List of Foils Used 

CPS615-Master95          Miscellaneous CPS615 Foils
3 4 
CPS615Eigs95             CPS615 Foils on  Matrices -- Eigenvalues and 
                          Vectors
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 
CPS615FEMetc95           CPS615 Foils on Finite Element Methods, Gauss
                           Seidel, Conjugate Gradient and Differential
                           Operators
1 2 3 4 5
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