In the nearly seven years since I finished writing the first edition of this book research on the
accuracy and stability of numerical algorithms has continued to flourish and mature. Our …

2 Introduction that the law of formation has been found. The corresponding direct problem is
to evaluate the sequence (an) given the law of formation. It is clear that such inverse …

The conjugate gradient method is a powerful tool for the iterative solution of self-adjoint
operator equations in Hilbert space. This volume summarizes and extends the …

This book deals with numerical methods for solving large sparse linear systems of
equations, particularly those arising from the discretization of partial differential equations. It …

We analyze the conjugate gradient (CG) method with preconditioning slightly variable from
one iteration to the next. To maintain the optimal convergence properties, we consider a …

The Lanczos and conjugate gradient algorithms were introduced more than five decades
ago as tools for numerical computation of dominant eigenvalues of symmetric matrices and …

The Lanczos algorithm is one of the most frequently used numerical methods for computing
a few eigenvalues (and eventually eigenvectors) of a large sparse symmetric matrix A. If the …

A new matrix decomposition of the form A= UTU+ UTR+ RTU is proposed and investigated,
where U is an upper triangular matrix (an approximation to the exact Cholesky factor U0) …

The problem of solving large, sparse, linear systems of algebraic equations is vital in
scientific computing, even for applications originating from quite different fields. A Survey of …

In their paper published in 1952, Hestenes and Stiefel considered the conjugate gradient
(CG) method an iterative method which terminates in at most n steps if no rounding errors …