Related papers: Error Inhibiting Block One-Step Schemes for Ordina…
In order to quantitatively study the accuracy of the unconditionally stable coarsening algorithms, we calculate the Fourier space multi step error on the order parameter field by explicitly distinguishing the analytic time $\tau$ and the…
We consider high-order splitting schemes for large-scale differential Riccati equations. Such equations arise in many different areas and are especially important within the field of optimal control. In the large-scale case, it is critical…
The ubiquitous backpropagation algorithm requires sequential updates through the network introducing a locking problem. In addition, back-propagation relies on the transpose of forward weight matrices to compute updates, introducing a…
In the paper [Muhammad Aslam Noor, Khalida Inayat Noor, Three-step iterative methods for nonlinear equations, Applied Mathematics and Computation, 183 (2006), pp. 322-327 ], Authors presented an algorithm (\textbf{Algorithm 2.3}) and stated…
Arising in semi-parametric statistics, control applications, and as sub-problems in global optimization methods, certain optimization problems can have objective functions requiring numerical integration to evaluate, yet gradient function…
Higher-order numerical methods are used to find accurate numerical solutions to hyperbolic partial differential equations and equations of transport type. Limiting is required to either converge to the correct type of solution or to adhere…
Global instability analysis of flows is often performed via time-stepping methods, based on the Arnoldi algorithm. When setting up these methods, several computational parameters must be chosen, which affect intrinsic errors of the…
We study the convergence rate of a class of linear multi-step methods for BSDEs. We show that, under a sufficient condition on the coefficients, the schemes enjoy a fundamental stability property. Coupling this result to an analysis of the…
Majorization-minimization schemes are a broad class of iterative methods targeting general optimization problems, including nonconvex, nonsmooth and stochastic. These algorithms minimize successively a sequence of upper bounds of the…
In this paper we extend the polynomial time integration framework to include exponential integration for both partitioned and unpartitioned initial value problems. We then demonstrate the utility of the exponential polynomial framework by…
In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…
Model order reduction involves constructing a reduced-order approximation of a high-order model while retaining its essential characteristics. This reduced-order model serves as a substitute for the original one in various applications such…
The Alekseev-Gr{\"o}bner lemma is combined with the theory of modified equations to obtain an \emph{a priori} estimate for the global error of numerical integrators. This estimate is correct up to a remainder term of order $h^{2p}$, where…
In this article, a posteriori error analysis of the elliptic obstacle problem is addressed using hybrid high-order methods. The method involve cell unknowns represented by degree-$r$ polynomials and face unknowns represented by degree-$s$…
The automatic selection of an appropriate time step size has been considered extensively in the literature. However, most of the strategies developed operate under the assumption that the computational cost (per time step) is independent of…
This paper is the second in a series of works on weak convergence of one-step schemes for solving stochastic differential equations (SDEs) with one-sided Lipschitz conditions. It is known that the super-linear coefficients may lead to a…
This paper discusses the error estimation of the last-column-block-augmented northwest-corner truncation (LC-block-augmented truncation, for short) of block-structured Markov chains (BSMCs) in continuous time. We first derive upper bounds…
There is a growing cross-disciplinary effort in the broad domain of optimization and learning with streams of data, applied to settings where traditional batch optimization techniques cannot produce solutions at time scales that match the…
In this paper we construct a third order method for solving additively split autonomous stiff systems of ordinary differential equations. The constructed additive method is L-stable with respect to the implicit part and allows to use an…
Descriptions of quantum algorithms, communication etc. protocols assume the existence of closed quantum system. However, real life quantum systems are open and are highly sensitive to errors. Hence error correction is of utmost importance…