Related papers: A nested Krylov subspace method for the overlap op…
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…
A general framework for oblique projections of nonhermitian matrices onto rational Krylov subspaces is developed. To obtain this framework we revisit the classical rational Krylov subspace algorithm and prove that the projected matrix can…
In the presence of a non-vanishing chemical potential the eigenvalues of the Dirac operator become complex. We calculate spectral correlation functions of complex eigenvalues using a random matrix model approach. Our results apply to…
We describe an explicit construction of approximate Ginsparg-Wilson fermions for QCD. We use ingredients of perfect action origin, and further elements. The spectrum of the lattice Dirac operator reveals the quality of the approximation. We…
Randomized Krylov subspace methods that employ the sketch-and-solve paradigm to substantially reduce orthogonalization cost have recently shown great promise in speeding up computations for many core linear algebra tasks (e.g., solving…
Subspace recycling iterative methods and other subspace augmentation schemes are a successful extension to Krylov subspace methods in which a Krylov subspace is augmented with a fixed subspace spanned by vectors deemed to be helpful in…
We consider a Krylov subspace approximation method for the symmetric differential Riccati equation $\dot{X} = AX + XA^T + Q - XSX$, $X(0)=X_0$. The method we consider is based on projecting the large scale equation onto a Krylov subspace…
We construct new Ginsparg-Wilson fermions for QCD by inserting an approximately chiral Dirac operator - which involves ingredients of a perfect action - into the overlap formula. This accelerates the convergence of the overlap Dirac…
The chiral symmetry at finite lattice spacing of Ginsparg-Wilson fermionic actions constrains the renormalization of the lattice operators; in particular, the topological susceptibility does not require any renormalization, when using a…
In this work we introduce a memory-efficient method for computing the action of a Hermitian matrix function on a vector. Our method consists of a rational Lanczos algorithm combined with a basis compression procedure based on rational…
The resolvent Krylov subspace method builds approximations to operator functions $f(A)$ times a vector $v$. For the semigroup and related operator functions, this method is proved to possess the favorable property that the convergence is…
It was recently proposed by the second author to consider lattice formulations of QCD in which complete actions, including the gauge part, are built explicitly from a given Dirac operator D. In a simple example of such theory, the gauge…
Thus far, sparse representations have been exploited largely in the context of robustly estimating functions in a noisy environment from a few measurements. In this context, the existence of a basis in which the signal class under…
Randomized orthogonal projection methods (ROPMs) can be used to speed up the computation of Krylov subspace methods in various contexts. Through a theoretical and numerical investigation, we establish that these methods produce…
Using the overlap-Dirac operator proposed by Neuberger, we have computed in lattice QCD the one-loop renormalization factors of ten operators which measure the lowest two moments of unpolarized and polarized non-singlet quark distributions.…
We present non-perturbative renormalization constants of fermionic bilinears on the lattice in the quenched approximation at beta=6.1 using an overlap fermion action with hypercubic(HYP)-blocked links. We consider the effects of the exact…
Iterative Krylov projection methods have become widely used for solving large-scale linear inverse problems. However, methods based on orthogonality include the computation of inner-products, which become costly when the number of…
The overlap hypercube fermion is a variant of a chirally symmetric lattice fermion, which is endowed with a higher level of locality than the standard overlap fermion. We apply this formulation in quenched QCD simulations with light quarks.…
The low-lying eigenvalues of a (sparse) hermitian matrix can be computed with controlled numerical errors by a conjugate gradient (CG) method. This CG algorithm is accelerated by alternating it with exact diagonalisations in the subspace…
We propose a fast algorithm for computing the entire ridge regression regularization path in nearly linear time. Our method constructs a basis on which the solution of ridge regression can be computed instantly for any value of the…