Related papers: Extrapolating the Arnoldi Algorithm To Improve Eig…

In this paper, we propose a new trigonometric interpolation algorithm and establish relevant convergent properties. The method adjusts an existing trigonometric interpolation algorithm such that it can better leverage Fast Fourier Transform…

The advantage that many quantum algorithms have over their classical counterparts may be lost when the results are extracted as classical data (output problem). One example are eigenpair solvers, which encode the eigenpairs in a quantum…

Error estimates for the numerical solution of the master equation are presented. Estimates are based on adjoint methods. We find that a good estimate can often be computed without spending computational effort on a dual problem. Estimates…

We consider Arnoldi like processes to obtain symplectic subspaces for Hamiltonian systems. Large systems are locally approximated by ones living in low dimensional subspaces; we especially consider Krylov subspaces and some extensions. This…

The numerical computation of matrix functions such as $f(A)V$, where $A$ is an $n\times n$ large and sparse square matrix, $V$ is an $n \times p$ block with $p\ll n$ and $f$ is a nonlinear matrix function, arises in various applications…

The estimation of weather forecast uncertainty with ensemble systems requires a careful selection of perturbations to establish a reliable sampling of the error growth potential in the phase space of the model. Usually, the singular vectors…

The iterated Arnoldi-Tikhonov (iAT) method is a regularization technique particularly suited for solving large-scale ill-posed linear inverse problems. Indeed, it reduces the computational complexity through the projection of the…

This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a…

This work considers the effect of averaging, and more generally extrapolation, of the iterates of gradient descent in smooth convex optimization. After running the method, rather than reporting the final iterate, one can report either a…

In this paper, we propose a novel extrapolation coefficient scheme within a new extrapolation term and develop an accelerated proximal gradient algorithm. We establish that the algorithm achieves a sublinear convergence rate. The proposed…

When used to accelerate the convergence of fixed-point iterative methods, such as the Picard method, which is a kind of nonlinear fixed-point iteration, polynomial extrapolation techniques can be very effective. The numerical solution of…

Vandermonde matrices are exponentially ill-conditioned, rendering the familiar "polyval(polyfit)" algorithm for polynomial interpolation and least-squares fitting ineffective at higher degrees. We show that Arnoldi orthogonalization fixes…

An inverse problem of finding an unknown heat source for a class of linear parabolic equations is considered. Such problems can typically be converted to a direct problem with non-local conditions in time instead of an initial value…

We propose a new numerical method to solve linear ordinary differential equations of the type $\frac{\partial u}{\partial t}(t,\varepsilon) = A(\varepsilon) \, u(t,\varepsilon)$, where $A:\mathbb{C}\rightarrow\mathbb{C}^{n\times n}$ is a…

This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each…

We study a stability preserved Arnoldi algorithm for matrix exponential in the time domain simulation of large-scale power delivery networks (PDN), which are formulated as semi-explicit differential algebraic equations (DAEs). The solution…

We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter…

The quantum mechanical expression relating two commuting operators is reformulated such that the power method (also called method of moments) for iteratively calculating eigenvalues and eigenvectors becomes applicable. The new iterative…

Constructing more expressive ansatz has been a primary focus for quantum Monte Carlo, aimed at more accurate \textit{ab initio} calculations. However, with more powerful ansatz, e.g. various recent developed models based on neural-network…

This paper introduces a new strategy for setting the regularization parameter when solving large-scale discrete ill-posed linear problems by means of the Arnoldi-Tikhonov method. This new rule is essentially based on the discrepancy…