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September 23, 2023

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This course includes:

Unlimited Duration

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Description

Numerical Linear Algebra. Instructors: Dr. P. N. Agrawal and Dr. D. N. Pandey, Department of Mathematics, IIT Roorkee.

This course covers lessons in basics of matrix algebra, computer arithmetic, conditioning and condition number, stability of numerical algorithms, vector and matrix norms, convergent matrices, stability of nonlinear systems, sensitivity analysis, singular value decomposition (SVD), algebraic and geometric properties of SVD, least square solutions, Householder matrices and applications, QR method, Power method and applications, Jacobi method for finding the eigenvalues of a given matrix. This course has tremendous applications in diverse fields of Engineering and Sciences such as control theory, image processing, numerical analysis and dynamical systems etc. (from nptel.ac.in)

Course Curriculum

  • Lecture 01 – Matrix Operations and Types of Matrices Unlimited
  • Lecture 02 – Determinant of a Matrix Unlimited
  • Lecture 03 – Rank of a Matrix Unlimited
  • Lecture 04 – Vector Space Unlimited
  • Lecture 05 – Vector Space (cont.) Unlimited
  • Lecture 06 – Linear Dependence and Independence Unlimited
  • Lecture 07 – Bases and Dimensions Unlimited
  • Lecture 08 – Bases and Dimensions (cont.) Unlimited
  • Lecture 09 – Linear Transformation Unlimited
  • Lecture 10 – Linear Transformation (cont.) Unlimited
  • Lecture 11 – Orthogonal Subspaces Unlimited
  • Lecture 12 – Row Space, Column Space and Null Space Unlimited
  • Lecture 13 – Eigenvalues and Eigenvectors Unlimited
  • Lecture 14 – Eigenvalues and Eigenvectors (cont.) Unlimited
  • Lecture 15 – Diagonalizable Matrices Unlimited
  • Lecture 16 – Orthogonal Sets Unlimited
  • Lecture 17 – Gram Schmidt Orthogonalization and Orthonormal Bases Unlimited
  • Lecture 18 – Introduction to MATLAB Unlimited
  • Lecture 19 – Sign Integer Representation Unlimited
  • Lecture 20 – Computer Representation of Numbers Unlimited
  • Lecture 21 – Floating Point Representation Unlimited
  • Lecture 22 – Round-off Error Unlimited
  • Lecture 23 – Error Propagation in Computer Arithmetic Unlimited
  • Lecture 24 – Addition and Multiplication of Floating Point Numbers Unlimited
  • Lecture 25 – Conditioning and Condition Numbers Unlimited
  • Lecture 26 – Conditioning and Condition Numbers (cont.) Unlimited
  • Lecture 27 – Stability of Numerical Algorithms Unlimited
  • Lecture 28 – Stability of Numerical Algorithms (cont.) Unlimited
  • Lecture 29 – Vector Norms Unlimited
  • Lecture 30 – Vector Norms (cont.) Unlimited
  • Lecture 31 – Matrix Norms Unlimited
  • Lecture 32 – Matrix Norms (cont.) Unlimited
  • Lecture 33 – Convergent Matrices Unlimited
  • Lecture 34 – Convergent Matrices (cont.) Unlimited
  • Lecture 35 – Stability of Nonlinear System Unlimited
  • Lecture 36 – Condition Number of A Matrix: Elementary Properties Unlimited
  • Lecture 37 – Sensitivity Analysis Unlimited
  • Lecture 38 – Sensitivity Analysis (cont.) Unlimited
  • Lecture 39 – Residual Theorem Unlimited
  • Lecture 40 – Nearness to Singularity Unlimited
  • Lecture 41 – Estimation of Condition Number Unlimited
  • Lecture 42 – Singular Value Decomposition of a Matrix Unlimited
  • Lecture 43 – Singular Value Decomposition of a Matrix (cont.) Unlimited
  • Lecture 44 – Orthogonal Projections Unlimited
  • Lecture 45 – Algebraic and Geometric Properties of Matrices using SVD Unlimited
  • Lecture 46 – SVD and their Applications Unlimited
  • Lecture 47 – Perturbation Theorem for Singular Values Unlimited
  • Lecture 48 – Outer Product Expansion of a Matrix Unlimited
  • Lecture 49 – Least Square Solutions Unlimited
  • Lecture 50 – Least Square Solutions (cont.) Unlimited
  • Lecture 51 – Householder Matrices Unlimited
  • Lecture 52 – Householder Matrices and their Applications Unlimited
  • Lecture 53 – Householder QR Factorization Unlimited
  • Lecture 54 – Householder QR Factorization (cont.) Unlimited
  • Lecture 55 – Basic Theorems on Eigenvalues and QR Method Unlimited
  • Lecture 56 – Power Method Unlimited
  • Lecture 57 – Rate of Convergence of Power Method Unlimited
  • Lecture 58 – Applications of Power Method with Shift Unlimited
  • Lecture 59 – Jacobi Method Unlimited
  • Lecture 60 – Jacobi Method (cont.) Unlimited

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