Related papers: A general class of iterative splitting methods for…
The splitting method is a powerful method for solving partial differential equations. Various splitting methods have been designed to separate different physics, nonlinearities, and so on. Recently, a new splitting approach has been…
Scalable Gaussian process (GP) inference is essential for sequential decision-making tasks, yet improving GP scalability remains a challenging problem with many open avenues of research. This paper focuses on iterative GPs, where iterative…
The Eberlein method is a Jacobi-type process for solving the eigenvalue problem of an arbitrary matrix. In each iteration two transformations are applied on the underlying matrix, a plane rotation and a non-unitary elementary…
Arnoldi method and conjugate gradient method are important classical iteration methods in solving linear systems and estimating eigenvalues. Their efficiency often affected by the high dimension of the space, where quantum computer can play…
In this paper, we propose variants of forward-backward splitting method for solving the system of splitting inclusion problem. We propose a conceptual algorithm containing three variants, each having a different projection steps. The…
Through introducing a new iterative formula for divided differnce using Neville's and Aitken's algorithms,we study new iterative methods for interpolation,numerical differentiation and numerical integration formulas with arbitrary order of…
Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…
Recently, inverse problems have attracted more and more attention in computational mathematics and become increasingly important in engineering applications. After the discretization, many of inverse problems are reduced to linear systems.…
Linear systems are the bedrock of virtually all numerical computation. Machine learning poses specific challenges for the solution of such systems due to their scale, characteristic structure, stochasticity and the central role of…
We consider adaptive finite element methods for second-order elliptic PDEs, where the arising discrete systems are not solved exactly. For contractive iterative solvers, we formulate an adaptive algorithm which monitors and steers the…
In this paper, we introduce a split general quasi-variational inequality problem which is a natural extension of split variational inequality problem, quasi-variational and variational inequality problems in Hilbert spaces. Using projection…
Jacobi-type algorithms for simultaneous approximate diagonalization of real (or complex) symmetric tensors have been widely used in independent component analysis (ICA) because of their good performance. One natural way of choosing the…
In this article, we establish a class of new projected type iteration methods based on matrix spitting for solving the linear complementarity problem. Also, we provide a sufficient condition for the convergence analysis when the system…
There are thousands of papers on rootfinding for nonlinear scalar equations. Here is one more, to talk about an apparently new method, which I call ``Inverse Cubic Iteration'' (ICI) in analogy to the Inverse Quadratic Iteration in Richard…
The indefinite least squares (ILS) problem is a generalization of the famous linear least squares problem. It minimizes an indefinite quadratic form with respect to a signature matrix. For this problem, we first propose an impressively…
In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow can not be computed exactly. Instead, we use a numerical…
We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…
An inexact framework of the Newton-based matrix splitting (INMS) iterative method is developed to solve the generalized absolute value equation, whose exact version was proposed by Zhou, Wu and Li [H.-Y. Zhou, S.-L. Wu and C.-X. Li,…
We present a stationary iteration method, namely Alternating Symmetric positive definite and Scaled symmetric positive semidefinite Splitting (ASSS), for solving the system of linear equations obtained by using finite element discretization…
This paper presents a unifying theory of Linear second order systems that allows time-varying and time invariant systems to be treated in the same way for the first time. In the process, a transformation is given that diagonalizes an…