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
