相关论文: Solving Symmetric and Positive Definite Second-Ord…

We have recently presented a method to solve an overdetermined linear system of equations with multiple right hand side vectors, where the unknown matrix is to be symmetric and positive definite. The coefficient and the right hand side…

Developing efficient solvers for large-scale multi-term linear matrix equations remains a central challenge in numerical linear algebra and is still largely unresolved. This paper introduces a methodology leveraging CUR decomposition for…

Functional data registration is a critical challenge in modern statistics, essential for separating phase variability from amplitude variability. While derivative-based frameworks offer mathematically elegant solutions, their dependence on…

In this paper, we present a novel method for solving multiobjective linear programming problems (MOLPP) that overcomes the need to calculate the optimal value of each objective function. This method is a follow-up to our previous work on…

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…

Matrix completion results deal with the question of when a partially specified symmetric matrix can be completed to a member of certain matrix cones. Results from positive semidefinite matrix completion and completely positive matrix…

In kernel methods, the kernels are often required to be positive definite, which restricts the use of many indefinite kernels. To consider those non-positive definite kernels, in this paper, we aim to build an indefinite kernel learning…

A new algorithm is presented for computing a direct solution to a system of consistent linear equations. It produces a minimum norm particular solution, a generalized inverse (of type {124}), and a null space projection operator. In…

In this work we propose a new method for investigating connection problems for the class of nonlinear second-order differential equations known as the Painlev{\'e} equations. Such problems can be characterized by the question as to how the…

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…

The concept of dispatchable region is useful in quantifying how much renewable generation power the system can handle. In this paper, we aim to provide an improved dispatchable region approximation method in distribution networks. First,…

We derive an efficient algorithm to find solutions to Euler's concordant form problem and rational points on elliptic curves associated with this problem.

We investigate the regularizing behavior of an iterative Krylov subspace method for the solution of linear inverse problems in precisions lower than double. Recent works have considered the projection of iterated Tikhonov methods using…

We devise a scheme for solving an iterative sequence of linear programs (LPs) or second order cone programs (SOCPs) to approximate the optimal value of any semidefinite program (SDP) or sum of squares (SOS) program. The first LP and…

We present a preconditioner based on spectral projection that is combined with a deflated Krylov subspace method for solving ill conditioned linear systems of equations. Our results show that the proposed algorithm requires many fewer…

CG, SYMMLQ, and MINRES are Krylov subspace methods for solving symmetric systems of linear equations. When these methods are applied to an incompatible system (that is, a singular symmetric least-squares problem), CG could break down and…

Tikhonov regularization is a widely used technique in solving inverse problems that can enforce prior properties on the desired solution. In this paper, we propose a Krylov subspace based iterative method for solving linear inverse problems…

Elliptic partial differential equations must be solved numerically for many problems in numerical relativity, such as initial data for every simulation of merging black holes and neutron stars. Existing elliptic solvers can take multiple…

Although a unique solution is guaranteed in the Linear complementarity problem (LCP) when the matrix $\mathbf{M}$ is positive definite, practical applications often involve cases where $\mathbf{M}$ is only positive semi-definite, leading to…

This paper reformulates complementarity-based time-stepping for frictionless nonsmooth contact between smooth rigid bodies as a recursively generated linear complementarity problem (ReLCP), involving a sequence of LCPs of increasing…