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Lecture Notes

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• Set number 14 : Full size: PDF.   Reduced: PDF .   Posted on: Mon 02 Dec 2024 04:39:40 PM CST (Last set of notes)
  Topics: Eigenvalue algorithms; Power method; The QR algorithm; Practical variants; Use of Hesseberg form ; Implicit Q theorem; QR algorithm for symmetric matrices.
      Supplement: Solutions to exercises and more. PDF    

• Set number 13 : Full size: PDF.   Reduced: PDF .   Posted on: Sun 01 Dec 2024 02:20:11 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: Wed Nov 20 05:21:00 PM CST 2024
  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 11 Nov 2024 04:33:41 PM CST
  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 10 : Full size: PDF.   Reduced: PDF .   Posted on: Mon 04 Nov 2024 12:40:52 PM CST
  Topics: Introduction to the Singular Value Decomposition. The singular value decomposition and its properties.
      Supplement: Solutions to exercises and more. PDF    

• Set number 9 : Full size: PDF.   Reduced: PDF .   Posted on: Mon 28 Oct 2024 10:06:31 AM 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 8 : Full size: PDF.   Reduced: PDF .   Posted on: Mon 21 Oct 2024 06:45:22 PM 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 7 : Full size: PDF.   Reduced: PDF .   Posted on: Mon 14 Oct 2024 06:33:38 PM CDT
  Topics: Positive Definiteness; Symmetric Positive Matrices; The LDLT and Cholesky factorizations.
      Supplement: Solutions to exercises and more. PDF    

• Set number 6 : Full size: PDF.   Reduced: PDF .   Posted on: Thu Oct 10 12:15:35 PM CDT 2024
  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 5 : Full size: PDF.   Reduced: PDF .   Posted on: Tue Oct 1 10:37:58 AM CDT 2024
  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 4 : Full size: PDF.   Reduced: PDF .   Posted on: Mon 23 Sep 2024 03:51:53 PM CDT
  Topics: Solving Linear Systems; Background; Gaussian Elimination (review); Gauss-Jordan; The LU factorization; Pivoting.
      Supplement: Solutions to exercises and more. PDF    

• Set number 3 : Full size: PDF.   Reduced: PDF .   Posted on: Tue Sep 10 10:02:30 AM CDT 2024
  Topics: Inner products and norms; Vector norms; Convergence of vector sequences; Matrix norms.
      Supplement: Solutions to exercises and more. PDF    

• Set number 2 : Full size: PDF.   Reduced: PDF .   Posted on: Thu 05 Sep 2024 06:37:41 AM CDT
  Topics: Matrices. Types of matrices. Matrices with structure; Special Matrices (Vandermonde, Toeplitz, Circulant, ..); Introduction to tensors.
      Supplement: Solutions to exercises and more. PDF    

• Set number 1 : Full size: PDF.   Reduced: PDF .   Posted on: Mon 02 Sep 2024 10:00:39 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 2024