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Course11110541763 lectures

Numerical Linear Algebra and Application

Prof. Srinivasa Rao Pentyala · IIT-ISM Dhanbad

Start with lecture 1 At NPTEL

Lectures

Week 1 :

  1. Lecture 01 : Linear Algebra and Introduction Video
  2. Lecture 02 : Computational Difficulties Video
  3. Lecture 03 : Computational Error Video
  4. Lecture 04 : Stability Video
  5. Lecture 05: Gaussian Elimination Video

Week 2 :

  1. Lecture 06 : LU Factorization Video
  2. Lecture 07 : Iterative refinement Video
  3. Lecture 08 : QR Factorization Video
  4. Lecture 09 : Gram-Schmidt Orthogonalization Video
  5. Lecture 10 : Cholesky Decomposition Video

Week 3 :

  1. Lecture 11: Projections Video
  2. Lecture 12 : House-Holder Reflectors Video
  3. Lecture 13 : Image Compression Video
  4. Lecture 14 : Singular Value Decomposition Video
  5. Lecture 15 : Least Square Solutions Video

Week 4 :

  1. Lecture 16 : Pseudo-Inverse Video
  2. Lecture 17 : Normal Equations Video
  3. Lecture 18 : Eigenvalue problems Video
  4. Lecture 19 : Gershgorin Theorem Video
  5. Lecture 20 : Similarity Transforms Video

Week 5 :

  1. Lecture 21 : Eigenvalues Video
  2. Lecture 22 : Sensitivity Vectors Video
  3. Lecture 23 : Power method Video
  4. Lecture 24 : Schur Decomposition Video
  5. Lecture 25 : Jordan Canonical form Video

Week 6 :

  1. Lecture 26 : QR Iteration Video
  2. Lecture 27 : Heisenberg transformation Video
  3. Lecture 28 : Rayleigh Quotient Video
  4. Lecture 29 : Symmetric eigenvalue problem Video
  5. Lecture 30 : Jacobi Method Video

Week 7 :

  1. Lecture 31 : Divide and Conquer Video
  2. Lecture 32 : Computing the Singular Value Decomposition Video
  3. Lecture 33 : Golub-Kahan-Reinsch Algorithm Video
  4. Lecture 34 : Chan SVD Algorithm Video
  5. Lecture 35 : Generalized SVD Video

Week 8 :

  1. Lecture 36 : Generalized and Quadratic Eigenvalue Problems Video
  2. Lecture 37 : Generalized Schur Decomposition (QZ Decomposition) Video
  3. Lecture 38 : Iterative Methods for Large Linear Systems: Jacobi Video

Week 9 :

  1. Lecture 39 : Iterative methods for large linear systems: Gauss-Seidel method Video
  2. Lecture 40 : Iterative methods for large linear systems: SOR method Video
  3. Lecture 41 : Convergence of iterative algorithms Video
  4. Lecture 42 : Krylov subspace methods Video
  5. Lecture 43 : Lanczos Video
  6. Lecture 44 : Arnoldi Video
  7. Lecture 45 : Stability of the Cholesky QR Algorithm Video

Week 10 :

  1. Lecture 46 : Conditioning of the eigenvalues Video
  2. Lecture 47 : Symmetric definite pencil Video
  3. Lecture 48 : AI applications Video
  4. Lecture 49 : Sensitive systems Video
  5. Lecture 50 : Real Life Systems Video

Week 11 :

  1. Lecture 51 : Transient thermal systems Video
  2. Lecture 52 : Left Inverse Video
  3. Lecture 53 : Right Inverse Video
  4. Lecture 54 : Generalized Inverse Video
  5. Lecture 55 : Applications Video

Week 12 :

  1. Lecture 56 : Applications (Contd.) Video
  2. Lecture 57 : Applications (Contd.) Video
  3. Lecture 58 : Applications (Contd.) Video
  4. Lecture 59 : Applications (Contd.) Video
  5. Lecture 60 : Applications of the Matrices in Real Life Systems Video
  6. Lecture 61 : Matrices and Its Fundamentals: Recalling Examples Video
  7. Lecture 62 : Properties of Matrices: Recalling and Revision, Examples Video
  8. Lecture 63 : Matrices: Finite Digit Arithmetic: recalling and Examples Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT-ISM Dhanbad
Department
Mathematics
Teacher
Prof. Srinivasa Rao Pentyala
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Kharagpur.
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