Related papers: Using the RD rational Arnoldi method for exponenti…
The present work provides a comprehensive study of symmetric-conjugate operator splitting methods in the context of linear parabolic problems and demonstrates their additional benefits compared to symmetric splitting methods. Relevant…
Matrix differential Riccati equation (DRE) typically exhibits transient and steady-state phases, posing challenges for fixed-step time integration methods, which may lack accuracy during transients or oversample in steady regimes. In this…
In this study we propose a-posteriori error estimation results to approximate the precision loss in quantities of interests computed using reduced order models. To generate the surrogate models we employ Proper Orthogonal Decomposition and…
We consider the maximum-a-posteriori inference problem in discrete graphical models and study solvers based on the dual block-coordinate ascent rule. We map all existing solvers in a single framework, allowing for a better understanding of…
In this paper we partially settle our conjecture from [1] (math.SP/0701143) on roots of eigenpolynomials for degenerate exactly-solvable operators. Namely, for any such operator, we establish a lower bound (which supports our conjecture)…
This paper presents a mathematical analysis of a doubly degenerate parabolic equation and its application to the Richards equation using a bounded auxiliary variable. We establish the existence of weak solutions using semi-implicit time…
Optimizing neural networks with loss that contain high-dimensional and high-order differential operators is expensive to evaluate with back-propagation due to $\mathcal{O}(d^{k})$ scaling of the derivative tensor size and the…
In this article we use linear algebra to improve the computational time for the obtaining of Green's functions of linear differential equations with reflection (DER). This is achieved by decomposing both the `reduced' equation (the ODE…
By exploiting the error functions of explicit symplectic integrators for solving separable Hamiltonians, I show that it is possible to develop explicit, time-reversible symplectic integrators for solving non-separable Hamiltonians of the…
We are concerned with the problem of recovering the radial kernel $k$, depending also on time, in a parabolic integro-differential equation $$D_{t}u(t,x)={\cal A}u(t,x)+\int_0^t k(t-s,|x|){\cal B}u(s,x)ds +\int_0^t D_{|x|}k(t-s,|x|){\cal…
In this paper we extend the Residual Arnoldi method for calculating an extreme eigenvalue (e.g. largest real part, dominant,...) to the case where the matrices depend on parameters. The difference between this Arnoldi method and the…
In this paper we consider mean-field optimal control problems with selective action of the control, where the constraint is a continuity equation involving a non-local term and diffusion. First order optimality conditions are formally…
We are concerned with the arithmetic of solutions to ordinary or partial nonlinear differential equations which are algebraic in the indeterminates and their derivatives. We call these solutions D-algebraic functions, and their equations…
This paper investigates a class of non-autonomous highly oscillatory ordinary differential equations characterized by a linear component inversely proportional to a small parameter $\varepsilon$, with purely imaginary eigenvalues, and an…
We develop an operator approach to the integration of linear differential equations based on intertwining relations between differential operators. Conditions for the existence of intertwining operators are obtained, and it is shown that,…
Inverse problems use physical measurements along with a computational model to estimate the parameters or state of a system of interest. Errors in measurements and uncertainties in the computational model lead to inaccurate estimates. This…
Recovery type a posteriori error estimators are popular, particularly in the engineering community, for their computationally inexpensive, easy to implement, and generally asymptotically exactness. Unlike the residual type error estimators,…
We continue to investigate which polynomials can possibly occur as factors in the denominators of rational solutions of a given partial linear difference equation. In an earlier article we had introduced the distinction between periodic and…
This work deals with the a posteriori error estimates for the Darcy-Forchheimer problem. We introduce the corresponding variational formulation and discretize it by using the finite-element method. A posteriori error estimate with two types…
The Arnoldi-Tikhonov method is a well-established regularization technique for solving large-scale ill-posed linear inverse problems. This method leverages the Arnoldi decomposition to reduce computational complexity by projecting the…