Introduction to computational linear algebra. (2015)

• Record Type: Book
• Further Information: Note: Nabil Nassif, Jocelyne Erhel, Bernard Philippe.
• Authors: Nassif, Nabil; Erhel, Jocelyne, 1956-; Philippe, Bernard, 1948-
• Contents: 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.
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2015
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 512.50285; Algebras, Linear -- Data processing; Matrices
• Languages: English
• ISBNs: 9781482258738; 9781482258714; 9781482258721
• Related ISBNs: 9781482258691
• Notes: Note: Description based on CIP data; item not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.