相关论文: A CG Method for Multiple Right Hand Sides and Mult…

We present an acceleration of the well-established Krylov-Ritz methods to compute the sign function of large complex matrices, as needed in lattice QCD simulations involving the overlap Dirac operator at both zero and nonzero baryon…

At physical light quark masses, efficient linear solvers are crucial for carrying out the millions of inversions of the Dirac matrix required for obtaining high statistics in quark correlation functions. Adaptive algebraic multi-grid…

We describe a Lanczos-based algorithm for approximating the product of a rational matrix function with a vector. This algorithm, which we call the Lanczos method for optimal rational matrix function approximation (Lanczos-OR), returns the…

Quantum field theories underlie all of our understanding of the fundamental forces of nature. The are relatively few first principles approaches to the study of quantum field theories [such as quantum chromodynamics (QCD) relevant to the…

Quadratic forms of Hermitian matrix resolvents involve the solutions of shifted linear systems. Efficient iterative solutions use the shift-invariance property of Krylov subspaces The Hermitian Lanczos method reduces a given vector and…

In this work, we propose a robust and easily implemented algebraic multigrid method as a stand-alone solver or a preconditioner in Krylov subspace methods for solving either symmetric and positive definite or saddle point linear systems of…

We propose a new method for the approximate solution of the Lyapunov equation with rank-$1$ right-hand side, which is based on extended rational Krylov subspace approximation with adaptively computed shifts. The shift selection is obtained…

In recent years two Krylov subspace methods have been proposed for solving skew symmetric linear systems, one based on the minimum residual condition, the other on the Galerkin condition. We give new, algorithm-independent proofs that in…

Close to the chiral limit, many calculations in numerical lattice QCD can potentially be accelerated using low-mode deflation techniques. In this paper it is shown that the recently introduced domain-decomposed deflation subspaces can be…

Enlarged Krylov subspace methods and their s-step versions were introduced [7] in the aim of reducing communication when solving systems of linear equations Ax = b. These enlarged CG methods consist of enlarging the Krylov subspace by a…

The large systems of complex linear equations that are generated in QCD problems often have multiple right-hand sides (for multiple sources) and multiple shifts (for multiple masses). Deflated GMRES methods have previously been developed…

The need for large-scale electronic structure calculations arises recently in the field of material physics and efficient and accurate algebraic methods for large simultaneous linear equations become greatly important. We investigate the…

This survey concerns subspace recycling methods, a popular class of iterative methods that enable effective reuse of subspace information in order to speed up convergence and find good initial guesses over a sequence of linear systems with…

The Krylov subspace methods, being one category of the most important classical numerical methods for linear algebra problems, can be much more powerful when generalised to quantum computing. However, quantum Krylov subspace algorithms are…

In this text I present a couple of new principles and thereon based iterative methods for numerical solution of sequences of systems of linear equations with fixed system matrix and changing right-hand-sides. The use of the new methods is…

Lattice QCD calculations require significant computational effort, with the dominant fraction of resources typically spent in the numerical inversion of the Dirac operator. One of the simplest methods to solve such large and sparse linear…

Work on generalizing the deflated, restarted GMRES algorithm, useful in lattice studies using stochastic noise methods, is reported. We first show how the multi-mass extension of deflated GMRES can be implemented. We then give a deflated…

The method of block coordinate gradient descent (BCD) has been a powerful method for large-scale optimization. This paper considers the BCD method that successively updates a series of blocks selected according to a Markov chain. This kind…

Many problems in science and engineering fields require the solution of shifted linear systems. To solve such systems efficiently, the recycling BiCG (RBiCG) algorithm in [SIAM J. SCI. COMPUT, 34 (2012) 1925-1949] is extended in this paper.…

Modern graphics hardware is designed for highly parallel numerical tasks and promises significant cost and performance benefits for many scientific applications. One such application is lattice quantum chromodyamics (lattice QCD), where the…