相关论文: Implicitly Restarted Generalized Second-order Arno…

This article aims at advancing the recently introduced exponential method for renormalisation in perturbative quantum field theory. It is shown that this new procedure provides a meaningful recursive scheme in the context of the algebraic…

We propose a rational QZ method for the solution of the dense, unsymmetric generalized eigenvalue problem. This generalization of the classical QZ method operates implicitly on a Hessenberg, Hessenberg pencil instead of on a Hessenberg,…

We advocate a new approach of addressing hidden structure problems and finding efficient quantum algorithms. We introduce and investigate the Hidden Symmetry Subgroup Problem (HSSP), which is a generalization of the well-studied Hidden…

In the last years, Regev's reduction has been used as a quantum algorithmic tool for providing a quantum advantage for variants of the decoding problem. Following this line of work, the authors of [JSW+24] have recently come up with a…

New iterative methods for solving linear equations are presented that are easy to use, generalize good existing methods, and appear to be faster. The new algorithms mix two kinds of linear recurrence formulas. Older methods have either high…

Polynomial preconditioning can improve the convergence of the Arnoldi method for computing eigenvalues. Such preconditioning significantly reduces the cost of orthogonalization; for difficult problems, it can also reduce the number of…

Convex quadratic programming (QP) is an important class of optimization problem with wide applications in practice. The classic QP solvers are based on either simplex or barrier method, both of which suffer from the scalability issue…

Several tensor eigenpair definitions have been put forth in the past decade, but these can all be unified under generalized tensor eigenpair framework, introduced by Chang, Pearson, and Zhang (2009). Given mth-order, n-dimensional…

Accelerated first order methods, also called fast gradient methods, are popular optimization methods in the field of convex optimization. However, they are prone to suffer from oscillatory behaviour that slows their convergence when medium…

In this paper, we introduce HPR-QP, a dual Halpern Peaceman-Rachford (HPR) method designed for solving large-scale convex composite quadratic programming. One distinctive feature of HPR-QP is that, instead of working with the primal…

We present the first systematic work for deriving a posteriori error estimates for general non-polynomial basis functions in an interior penalty discontinuous Galerkin (DG) formulation for solving eigenvalue problems associated with second…

This paper investigates iterative methods for solving bi-level optimization problems where both inner and outer functions have a composite structure. We establish novel theoretical results, including the first analysis that provides…

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…

Gaussian processes are probabilistic models that are commonly used as functional priors in machine learning. Due to their probabilistic nature, they can be used to capture the prior information on the statistics of noise, smoothness of the…

In this paper, we consider a generalized multivariate regression problem where the responses are monotonic functions of linear transformations of predictors. We propose a semi-parametric algorithm based on the ordering of the responses…

Second-order cone programs (SOCPs) with quadratic objective functions are common in optimal control and other fields. Most SOCP solvers which use interior-point methods are designed for linear objectives and convert quadratic objectives…

In this work we consider a class of delay eigenvalue problems that admit a spectrum similar to that of a Hamiltonian matrix, in the sense that the spectrum is symmetric with respect to both the real and imaginary axis. More precisely, we…

We design a fast implicit real QZ algorithm for eigenvalue computation of structured companion pencils arising from linearizations of polynomial rootfinding problems. The modified QZ algorithm computes the generalized eigenvalues of an…

Maximizing the sum of two generalized Rayleigh quotients (SRQ) can be reformulated as a one-dimensional optimization problem, where the function value evaluations are reduced to solving semi-definite programming (SDP) subproblems. In this…

We propose an acceleration scheme for first-order methods (FOMs) for convex quadratic programs (QPs) that is analogous to Anderson acceleration and the Generalized Minimal Residual algorithm for linear systems. We motivate our proposed…