Related papers: Backward Stability of Explicit External Deflation …

In recently proposed stabilisation techniques for parabolic equations, a crucial role is played by a suitable sequence of oblique projections in Hilbert spaces, onto the linear span of a suitable set of M actuators, and along the subspace…

In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. The algorithm uses a variable stepsize which is updated at each iteration and based on some previous…

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…

Given an approximation to a multiple isolated solution of a polynomial system of equations, we have provided a symbolic-numeric deflation algorithm to restore the quadratic convergence of Newton's method. Using first-order derivatives of…

First, we consider the problem of hedging in complete binomial models. Using the discrete-time F\"ollmer-Schweizer decomposition, we demonstrate the equivalence of the backward induction and sequential regression approaches. Second, in…

The overall performance or expected excess risk of an iterative machine learning algorithm can be decomposed into training error and generalization error. While the former is controlled by its convergence analysis, the latter can be tightly…

The parallel orbital-updating approach is an orbital/eigenfunction iteration based approach for solving eigenvalue problems when many eigenpairs are required. It has been proven to be efficient, for instance, in electronic structure…

The stability and convergence rate of Olver's collocation method for the numerical solution of Riemann-Hilbert problems (RHPs) is known to depend very sensitively on the particular choice of contours used as data of the RHP. By manually…

This work provides a systematic study of the variational properties of decomposable functions which are compositions of an outer support function and an inner smooth mapping under certain constraint qualifications. A particular focus is put…

This paper introduces some efficient initials for a well-known algorithm (an inverse iteration) for computing the maximal eigenpair of a class of real matrices. The initials not only avoid the collapse of the algorithm but are also…

We introduce an efficient stable algorithm for transforms associated with expansions in Hermite functions interpolated at Hermite polynomial roots. The Hermite transform matrix can be factorised into a diagonal component and an orthogonal…

Transient stability assessment of power systems needs to account for increased risk from uncertainties due to the integration of renewables and distributed generators. The uncertain operating condition of the power grid hinders reliable…

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…

A lower bound on the solution to the traveling salesman problem is provided, which is expressed in terms of eigenvalues related to the distance matrix for the problem. This bound has many interesting properties such as transforming…

This paper presents a posteriori error estimates for conforming numerical approximations of eigenvalue clusters of second-order self-adjoint elliptic linear operators with compact resolvent. Given a cluster of eigenvalues, we estimate the…

The matter of the stability for multi-asset American option pricing problems is a present remaining challenge. In this paper a general transformation of variables allows to remove cross derivative terms reducing the stencil of the proposed…

We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit…

This paper investigates oscillation-free stability conditions of numerical methods for linear parabolic partial differential equations with some example extrapolations to nonlinear equations. Not clearly understood, numerical oscillations…

Numerically solving the 2D Helmholtz equation is widely known to be very difficult largely due to its highly oscillatory solution, which brings about the pollution effect. A very fine mesh size is necessary to deal with a large wavenumber…

One of the most used approaches in simulating materials is the tight-binding approximation. When using this method in a material simulation, it is necessary to compute the eigenvalues and eigenvectors of the Hamiltonian describing the…