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Lecture Notes

Note: Reduced means 4 viewgraphs per page. Full size is one per page.
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• Set number 13 : Full size: PDF.   Reduced: PDF .   Posted on: Fri Nov 30 11:03:07 CST 2018
  Topics: Eigenvalue problems (continued); The QR algorithm; Practical variants; Symmetric eigenvalue problems -Min-max theorem; The law of intertia; The QR algorithm for symmetric matrices; The Jacobi algorithm.

• Set number 12 : Full size: PDF.   Reduced: PDF .   Posted on: Sat Nov 17 09:30:46 CST 2018
  Topics: Eigenvalue problems; Brief background; the Schur form; Perturbation analysis; conditioning of a simple eigenvalues; The power method and related techniques.

• Set number 11 : Full size: PDF.   Reduced: PDF .   Posted on: Tue Nov 13 17:34:47 CST 2018
  Topics: A few applications of the SVD; Regularization; Information retrieval; Principal Component Analysis (PCA); Dimension reduction.

• Set number 10 : Full size: PDF.   Reduced: PDF .   Posted on: Sun Nov 11 14:52:31 CST 2018. * Reposted Nov. 14 with a few changes and additions *
  Topics: The singular value decomposition; Pseudo-inverses; Application to least-squares; Regularization.

• Set number 9 : Full size: PDF.   Reduced: PDF .   Posted on: Tue Nov 6 16:55:57 CST 2018
  Topics: Orthogonal subspaces & orthogonal projectors; Orthogonal decomposition; The 4 fundamental subspaces; the URV decomposition. Introduction to the Singular Value Decomposition.

• Set number 8 : Full size: PDF.   Reduced: PDF .   Posted on: Tue Oct 30 09:27:50 CDT 2018
  Topics: The Householder QR; the rank Deficient case; Computational cost; Solving Least-squares problems with the householder QR; Givens rotations and the Givens QR.

• Set number 7 : Full size: PDF.   Reduced: PDF .   Posted on: Sun Oct 28 17:17:23 CDT 2018
  Topics: The Gram-Schmidt algorithms and the QR Factorization; Least-squares problems; Applications; Data fitting;

• Set number 6 : Full size: PDF.   Reduced: PDF .   Posted on: Sun Oct 14 17:25:54 CDT 2018
  Topics: Positive Definiteness; Symmetric Positive Matrices; The LDLT and Cholesky factorizations; Banded systems

• Set number 5 : Full size: PDF.   Reduced: PDF .   Posted on: Tue Oct 9 07:32:46 CDT 2018
  Topics: Perturbation theory for linear systems; sensitivity analysis; Condition numbers; Error bounds; Norm-wise error analysis. Estimating cond. numbers Estimating forward errors from residual norms.

• Set number 4 : Full size: PDF.   Reduced: PDF .   Posted on: Tue Oct 2 17:26:16 CDT 2018
  Topics: Concepts in floating point arithmetic; Error analysis Forward and backward errors; Errors in inner products; Application to linear systems. Supplement: Floating point numbers; IEEE standard.

• Set number 3 : Full size: PDF.   Reduced: PDF .   Posted on: Mon Sep 17 10:46:37 CDT 2018
  Topics: Solving Linear Systems; Background; Gaussian Elimination (review); Gauss-Jordan; The LU factorization; Pivoting.

• Set number 2 : Full size: PDF.   Reduced: PDF .   Posted on: Tue Sep 11 11:59:58 CDT 2018
  Topics: Inner products and norms; Vector norms; Convergence of vector sequences; Matrix norms.

• Set number 1 : Full size: PDF.   Reduced: PDF .   Posted on: Tue Sep 4 10:47:57 CDT 2018
  Topics: Introduction; Types of problems seen in this course ; Math. background; Matrices; Eigenvalues and eigenvectors; Null space and range; Rank; Types of matrices; Special matrices.

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csci 5304 - Fall 2017