Matrix algorithms in MATLAB (Q2799469)

The book is concerned with the description of the matrix algorithms from MATLAB (MATrix LABoratory) software product, an interpretive computer language as well as a numerical computation environment. After a brief mathematical exposure, the algorithm is presented through the use of real computer codes. This ensures a better understanding of how an algorithm works, than by only studying their pseudo-codes as happens in classical algorithmic books. Beside the common decomposition type MATLAB algorithms the book contains over 15 different equation solution algorithms, over 10 different eigenvalue and singular value algorithms. All the codes presented in the book are tested with thousands of runs on MATLAB randomly generated matrices. The book covers only the real matrices class and do not consider the special cases of band and/or sparse matrices. It is structured in 8 chapters. Chapter 1 is a brief introduction in MATLAB and makes the reader familiar with the book's notations and the basic theory of matrix computations. Chapters 2 and 3 deal with decompositions of general matrices and special classes of matrices. The author presents LU, Cholesky, QR type decomposition together with Householder, Givens, Hessenberg, upper and lower triangular matrices. Chapter 4 is dedicated to direct solvers of linear systems of equations (Gauss type elimination and Householder and Givens type elimination methods), whereas Chapter 5 describes iterative linear solvers as Jacobi, Gauss-Seidel, 3 Lanczos based methods, 11 Arnoldi based ones and 4 special algorithms for normal equations. Moreover, its last section deals with preconditioning, algebraic multigrid and domain decomposition algorithms. Chapters 6 and 7 describe direct, respectively iterative algorithms for the numerical solution of eigenvalue problems. The author considers both symmetric and unsymmetric matrices, as well as specially structured ones (tri-diagonal, symmetric and unsymmetric positive definite pencils, and symmetric but indefinite pencils. The last Chapter 8 presents algorithms for computing the singular value decomposition (SVD) of a matrix -- Jacobi type, QR and Lanczos SVD algorithm.NEWLINENEWLINE The book is addressed to people working in the field of matrix computations, for efficient implementation and improvement of matrix algorithms: students of different degrees in computer science, applied mathematics and computational engineering, as well as researchers in numerical analysis, and computer engineering and scientific research.