NOC:Matrix Solver


Lecture 1 - Introduction to Matrix Algebra - I


Lecture 2 - Introduction to Matrix Algebra - II


Lecture 3 - System of Linear Equations


Lecture 4 - Determinant of a Matrix


Lecture 5 - Determinant of a Matrix (Continued...)


Lecture 6 - Gauss Elimination


Lecture 7 - Gauss Elimination (Continued...)


Lecture 8 - LU Decomposition


Lecture 9 - Gauss-Jordon Method


Lecture 10 - Representation of Physical Systems as Matrix Equations


Lecture 11 - Tridiagonal Matrix Algorithm


Lecture 12 - Equations with Singular Matrices


Lecture 13 - Introduction to Vector Space


Lecture 14 - Vector Subspace


Lecture 15 - Column Space and Nullspace of a Matrix


Lecture 16 - Finding Null Space of a Matrix


Lecture 17 - Solving Ax=b when A is Singular


Lecture 18 - Linear Independence and Spanning of a Subspace


Lecture 19 - Basis and Dimension of a Vector Space


Lecture 20 - Four Fundamental Subspaces of a Matrix


Lecture 21 - Left and right inverse of a matrix


Lecture 22 - Orthogonality between the subspaces


Lecture 23 - Best estimate


Lecture 24 - Projection operation and linear transformation


Lecture 25 - Creating orthogonal basis vectors


Lecture 26 - Gram-Schmidt and modified Gram-Schmidt algorithms


Lecture 27 - Comparing GS and modified GS


Lecture 28 - Introduction to eigenvalues and eigenvectors


Lecture 29 - Eigenvlues and eigenvectors for real symmetric matrix


Lecture 30 - Positive definiteness of a matrix


Lecture 31 - Positive definiteness of a matrix (Continued...)


Lecture 32 - Basic Iterative Methods: Jacobi and Gauss-Siedel


Lecture 33 - Basic Iterative Methods: Matrix Representation


Lecture 34 - Convergence Rate and Convergence Factor for Iterative Methods


Lecture 35 - Numerical Experiments on Convergence


Lecture 36 - Steepest Descent Method: Finding Minima of a Functional


Lecture 37 - Steepest Descent Method: Gradient Search


Lecture 38 - Steepest Descent Method: Algorithm and Convergence


Lecture 39 - Introduction to General Projection Methods


Lecture 40 - Residue Norm and Minimum Residual Algorithm


Lecture 41 - Developing computer programs for basic iterative methods


Lecture 42 - Developing computer programs for projection based methods


Lecture 43 - Introduction to Krylov subspace methods


Lecture 44 - Krylov subspace methods for linear systems


Lecture 45 - Iterative methods for solving linear systems using Krylov subspace methods


Lecture 46 - Conjugate gradient methods


Lecture 47 - Conjugate gradient methods (Continued...)


Lecture 48 - Conjugate gradient methods (Continued...) and Introduction to GMRES


Lecture 49 - GMRES (Continued...)


Lecture 50 - Lanczos Biorthogonalization and BCG Algorithm


Lecture 51 - Numerical issues in BICG and polynomial based formulation


Lecture 52 - Conjugate gradient squared and Biconjugate gradient stabilized


Lecture 53 - Line relaxation method


Lecture 54 - Block relaxation method


Lecture 55 - Domain Decomposition and Parallel Computing


Lecture 56 - Preconditioners


Lecture 57 - Preconditioned conjugate gradient


Lecture 58 - Preconditioned GMRES


Lecture 59 - Multigrid methods - I


Lecture 60 - Multigrid methods - II