C S C I 5 3 0 4
Lecture Notes
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- Set number 15 : Full size:
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Posted on:
Wed 07 Dec 2022 08:41:07 AM CST
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.
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Wed Nov 30 09:35:46 CST 2022
Topics:
Symmetric eigenvalue problems -Min-max theorem; The law of intertia;
The QR algorithm for symmetric matrices; The Jacobi algorithm.
Supplement: Solutions to exercises and more.
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Mon 28 Nov 2022 02:45:03 PM CST
Topics:
Eigenvalue problems (continued); The QR algorithm; Practical variants;
Use of Hesseberg form ; Implicit Q theorem;
QR algorithm for symmetric matrices.
Supplement: Solutions to exercises and more.
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Mon 21 Nov 2022 02:04:32 PM CST
Topics:
Eigenvalue problems; Brief background; the Schur form;
Perturbation analysis; conditioning of a simple eigenvalues;
The power method and related techniques.
Supplement: Solutions to exercises and more.
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Mon 14 Nov 2022 01:29:16 PM CST
Topics:
A few applications of the SVD; Regularization; Information retrieval;
Principal Component Analysis (PCA); Dimension reduction.
Supplement: Solutions to exercises and more.
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Wed Nov 9 08:50:28 CST 2022
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.
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Wed Nov 2 09:14:29 CDT 2022
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.
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Wed Oct 26 14:42:45 CDT 2022
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.
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Wed 19 Oct 2022 06:26:07 PM CDT
Topics:
The Gram-Schmidt algorithms and the QR Factorization;
Least-squares problems; Applications; Data fitting;
Supplement: Solutions to exercises and more.
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- Set number 6 : Full size:
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Wed Oct 12 16:18:46 CDT 2022
Topics:
Positive Definiteness; Symmetric Positive Matrices;
The LDLT and Cholesky factorizations.
Supplement: Solutions to exercises and more.
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Mon 10 Oct 2022 02:53:52 PM 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.
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Wed Sep 28 16:22:44 CDT 2022
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.
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Wed Sep 21 14:33:41 CDT 2022
Topics:
Solving Linear Systems; Background;
Gaussian Elimination (review); Gauss-Jordan;
The LU factorization; Pivoting.
Supplement: Solutions to exercises and more.
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Mon 12 Sep 2022 10:57:11 AM CDT
Topics:
Inner products and norms; Vector norms;
Convergence of vector sequences; Matrix norms.
Supplement: Solutions to exercises and more.
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- Set number 1 : Full size:
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Posted on:
Tue 06 Sep 2022 06:18:01 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.
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csci 5304 - Fall 2022