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Lecture Notes

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• Set number 15 : Full size: PDF.   Reduced: PDF .   Posted on: Tue Dec 5 15:12:09 CST 2023
  Topics: [Last set of notes] Large Sparse eigenvalue problems; Rayleigh-Ritz projection; Subspace iteration; Lanczos algorithms; Loss of orthogonality; Golub-Kahan-Lanczos bidiagonalization.
      Supplement: Solutions to exercises and more. PDF    

• Set number 14 : Full size: PDF.   Reduced: PDF .   Posted on: Wed 29 Nov 2023 09:50:58 AM CST
  Topics: Eigenvalue algorithms; Power method; The QR algorithm; Practical variants; Use of Hesseberg form ; Implicit Q theorem; QR algorithm for symmetric matrices; The Jacobi method
      Supplement: Solutions to exercises and more. PDF    

• Set number 13 : Full size: PDF.   Reduced: PDF .   Posted on: Sun 26 Nov 2023 05:16:44 PM CST
  Topics: Symmetric eigenvalue problems; General results; The min-max theorem; The law of intertia; Application: The bisection method.
      Supplement: Solutions to exercises and more. PDF    

• Set number 12 : Full size: PDF.   Reduced: PDF .   Posted on: Mon 20 Nov 2023 10:11:40 AM CST
  Topics: Eigenvalue problems; Brief background; Diagonalizable matrices; The Schur form; Gerschgorin's theorem; Perturbation analysis; conditioning of a simple eigenvalues;
      Supplement: Solutions to exercises and more. PDF    

• Set number 11 : Full size: PDF.   Reduced: PDF .   Posted on: Mon 20 Nov 2023 10:11:06 AM CST
  Topics: A few applications of the SVD; Regularization; Information retrieval; Principal Component Analysis (PCA); Dimension reduction.
      Supplement: Solutions to exercises and more. PDF    

• Set number 10 : Full size: PDF.   Reduced: PDF .   Posted on: Wed Nov 15 18:17:42 CST 2023
  Topics: The Pseudo inverse; Application to least-squares; Moore-Penrose Pseudo-in Ill-conditioned systems and the SVD; Numerical rank and the SVD;
      Supplement: Solutions to exercises and more. PDF    

• Set number 9 : Full size: PDF.   Reduced: PDF .   Posted on: Wed Nov 8 08:59:59 CST 2023
  Topics: Orthogonal subspaces & orthogonal projectors; Orthogonal decomposition; The 4 fundamental subspaces; the URV decomposition. Introduction to the Singular Value Decomposition. The singular value decomposition and its properties.
      Supplement: Solutions to exercises and more. PDF    

• Set number 8 : Full size: PDF.   Reduced: PDF .   Posted on: Mon 30 Oct 2023 03:26:14 PM CDT
  Topics: The Householder QR; the rank Deficient case; Computational cost; Solving Least-squares problems with the householder QR; Givens rotations and the Givens QR.
      Supplement: Solutions to exercises and more. PDF    

• Set number 7 : Full size: PDF.   Reduced: PDF .   Posted on: Mon 23 Oct 2023 11:22:19 AM CDT
  Topics: The Gram-Schmidt algorithms and the QR Factorization; Least-squares problems; Applications; Data fitting;
      Supplement: Solutions to exercises and more. PDF    

• Set number 6 : Full size: PDF.   Reduced: PDF .   Posted on: Mon 16 Oct 2023 03:51:38 PM CDT
  Topics: Positive Definiteness; Symmetric Positive Matrices; The LDLT and Cholesky factorizations.
      Supplement: Solutions to exercises and more. PDF    

• Set number 5 : Full size: PDF.   Reduced: PDF .   Posted on: Mon 09 Oct 2023 08:06:42 AM CDT
  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.
      Supplement: Solutions to exercises and more. PDF    

• Set number 4 : Full size: PDF.   Reduced: PDF .   Posted on: Wed Oct 4 11:49:25 CDT 2023
  Topics: Concepts in floating point arithmetic; Error analysis Forward and backward errors; Errors in inner products; Application to linear systems.
      Supplement: Solutions to exercises and more. PDF    

• Set number 3 : Full size: PDF.   Reduced: PDF .   Posted on: Wed Sep 20 14:48:39 CDT 2023
  Topics: Solving Linear Systems; Background; Gaussian Elimination (review); Gauss-Jordan; The LU factorization; Pivoting.
      Supplement: Solutions to exercises and more. PDF    

• Set number 2 : Full size: PDF.   Reduced: PDF .   Posted on: Mon 11 Sep 2023 12:22:01 PM CDT
  Topics: Inner products and norms; Vector norms; Convergence of vector sequences; Matrix norms.
      Supplement: Solutions to exercises and more. PDF    

• Set number 1 : Full size: PDF.   Reduced: PDF .   Posted on: Sun 03 Sep 2023 10:40:58 AM CDT
  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.
      Supplement: Solutions to exercises and more. PDF    

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csci 5304 - Fall 2023