Here is the listing of Best reference books on Matrix Computations.
1. “Iterative Solution Methods” by Owe Axelsson
Book Review: The book contains basic and classic methods that involve the study of linear algebra and numerical linear algebra. The book also deals with the construction of preconditioners and iterative acceleration methods of the conjugate gradient type. This book is very useful for graduate students and researchers in the field of numerical analysis and applied mathematics. This book is also useful for other areas where linear equation systems play an important role. The book also contains mathematical theory and concepts in the area of numerical linear algebra.


2. “Computer Solution of Large Linear Systems” by G. Meurant
Book Review: This book involves with the numerical methods which help in solving large sparse linear system of equations especially with the ones that involve discretization of partial differential equations. The book includes both direct and iterative methods. Direct methods include variants of Gaussian elimination which are helpful in solving differential equations in rectangular domains. The book also demonstrates classical iterative methods like Jacobi, gausssiedel and other direction algorithms. The book also contains a separate chapter on multigrid method and ends with domain decomposition algorithms.


3. “Matrix Computations” by Golub and C. Van Loan
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Book Review: This book is a very good textbook for computer science which contains very useful information covering the mathematical background and algorithmic skills which are used in the production of numerical software. The book contains revised chapters on matrix multiplication problems, parallel matrix computations, CS decomposition treatment, floating point arithmetic operations, gramschmidt process, concepts of GMRES, QMR and other methods which demonstrate the sparse unsymmetric linear system problems.


4. “Matrix Perturbation Theory” by G. W. Stewart and J. Sun
Book Review: This book deals with the concepts of matrix perturbation theory which are presented in the form of surveys. This book is very useful to numerical analysts, statisticians, physical scientists and engineers. The book also deals with the perturbation theory of linear students, least square problems, eigenvalue problems, generalized eigenvalue problems, vector and matrix norms which also includes theory of unitary invariant norms.


5. “Fundamentals of Matrix Computations” by Watkins D.S
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Book Review: This book deals with the basics of matrix computations, numerical linear algebra algorithms, algorithm development and their working. The book deals with francis QR algorithm, applications of gramschmidt algorithm using the concept of reorthogonalization, golubreinsch SVD algorithm derivation, eigenvalue product problem solving, Jacobidavidson method treatment, various iterative methods for linear equation solving. The book uses MATLAB to solve real world problems in electrical circuits, mass spring systems, simple partial differential equations, matrix computations and is suitable to researchers and practitioners working in the field of engineering and computer science.


6. “Introduction to Matrix Computations” by Stewart. G.W  
Sanfoundry Global Education & Learning Series – Best Reference Books!