Lecture 31 of 60Week 7
Lecture 31 : Positive definiteness of a matrix (Contd.)
Prof. Somnath Roy · IIT Kharagpur
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All the lectures
- Lecture 01 : Introduction to Matrix Algebra - I
- Lecture 02 : Introduction to Matrix Algebra - II
- Lecture 03 : System of Linear Equations
- Lecture 04 : Determinant of a Matrix
- Lecture 05 : Determinant of a Matrix (Contd.)
- Lecture 06 : Gauss Elimination
- Lecture 07 : Gauss Elimination(Contd.)
- Lecture 08 : LU Decomposition
- Lecture 09 : 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 (Contd.)
- 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(Contd.)
- Lecture 48 : Conjugate gradient methods(Contd.) and Introduction to GMRES
- Lecture 49 : GMRES (Contd.)
- 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