Matrix Multiplication Problems: Structure and Efficiency, Block Matrix and Algorithms, Fast Matrix vector products. Matrix Analysis: Vector Spaces, Norms, Matrix norms, Orthogonality, Singular value Decomposition, Sensitivity of Square systems, Finite precision matrix computation. Linear Systems: Triangular Systems, LU Factorization, Parallel LU, Diagonal Dominance and Symmetry, Positive Definite Systems, Banded Systems. Orthogonalizations and Least squares: Householder and Givens Transformation, QR Factorization.
Parallel Matrix Computation: Basic concepts, Cost of Communication, Challenge of Load Balancing, Tradeoffs, Shared Memory Systems, Parallel Matrix Multiplication. Eigen value Computation: Power Iteration, Jacobi Method.