Content: Basic Linear Algebra Subprograms: BLAS An Introductory Example Matrix Notations IEEE Floating Point Systems and Computer Arithmetic Vector-Vector Operations: Level-1 BLAS Matrix-Vector Operations: Level-2 BLAS Matrix-Matrix Operations: Level-3 BLAS Sparse Matrices: Storage and Associated Operations Basic Concepts for Matrix Computations Vector Norms Complements on Square Matrices Rectangular Matrices: Ranks and Singular Values Matrix Norms Gauss Elimination and LU Decompositions of Matrices Special Matrices for LU Decomposition Gauss Transforms Naive LU Decomposition for a Square Matrix with Principal Minor Property (pmp) Gauss Reduction with Partial Pivoting: PLU Decompositions MATLAB Commands Related to the LU Decomposition Condition Number of a Square Matrix Orthogonal Factorizations and Linear Least Squares Problems Formulation of Least Squares Problems: Regression Analysis Existence of Solutions Using Quadratic Forms Existence of Solutions through Matrix Pseudo-Inverse The QR Factorization Theorem Gram-Schmidt Orthogonalization: Classical, Modified, and Block Solving the Least Squares Problem with the QR Decomposition Householder QR with Column Pivoting MATLAB Implementations Algorithms for the Eigenvalue Problem Basic Principles QR Method for a Non-Symmetric Matrix Algorithms for Symmetric Matrices Methods for Large Size Matrices Singular Value Decomposition Iterative Methods for Systems of Linear Equations Stationary Methods Krylov Methods Method of Steepest Descent for spd Matrices Conjugate Gradient Method (CG) for spd Matrices The Generalized Minimal Residual Method The Bi-Conjugate Gradient Method Preconditioning Issues Sparse Systems to Solve Poisson Differential Equations Poisson Differential Equations The Path to Poisson Solvers Finite Differences for Poisson-Dirichlet Problems Variational Formulations One-Dimensional Finite-Element Discretizations Bibliography Index Exercises and Computer Exercises appear at the end of each chapter.