Direct and Iterative Linear System Solvers

An in-depth exploration of algorithms for solving nonsingular linear systems, detailing advanced elimination procedures, iterative solvers including conjugate gradients and Krylov methods, and emphasizing finite precision challenges and numerical experiments. Techniques like mixed precision and randomization also feature. Solving linear systems of equations is ubiquitous in scientific computing, therefore, the numerical algorithms for solving them are paramount. Direct and Iterative Linear System Solvers describes the state of the art of direct and iterative methods for solving nonsingular linear systems of equations. The author considers several variants of elimination methods; classical iterative methods; variants of the conjugate gradient method; and Krylov methods for non-symmetric systems and describes many preconditioners. Finite precision arithmetic and numerical experiments are emphasized. Direct and Iterative Linear System Solvers describes and analyzes many numerical experiments with these methods, introduces more recent techniques like mixed precision and randomization, and contains templates of codes for implementing these methods.