Related papers: Rational approximation preconditioners for multiph…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
The use of approximation is fundamental in computational science. Almost all computational methods adopt approximations in some form in order to obtain a favourable cost/accuracy trade-off and there are usually many approximations that…
Rational and neural network based approximations are efficient tools in modern approximation. These approaches are able to produce accurate approximations to nonsmooth and non-Lipschitz functions, including multivariate domain functions. In…
Understanding frictional phenomena is a fascinating fundamental problem with huge potential impact on energy saving. Such an understanding requires monitoring what happens at the sliding buried interface, which is almost inaccessible by…
We give necessary and sufficient topological conditions for a simple closed curve on a real rational surface to be approximable by smooth rational curves. We also study approximation by smooth rational curves with given complex…
A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We present a theorem that describes the…
A large system of ordinary differential equations is approximated by a parabolic partial differential equation with dynamic boundary condition and a different one with Robin boundary condition. Using the theory of differential operators…
The Operator axioms have produced new real numbers with new operators. New operators naturally produce new equations and thus extend the traditional mathematical models which are selected to describe various scientific rules. So new…
Given a set of matrices, modeled as samples of a matrix-valued function, we suggest a method to approximate the underline function using a product approximation operator. This operator extends known approximation methods by exploiting the…
We consider a mixed dimensional elliptic partial differential equation posed in a bulk domain with a large number of embedded interfaces. In particular, we study well-posedness of the problem and regularity of the solution. We also propose…
Following T. H. Chan, we consider the problem of approximation of a given rational fraction a/q by sums of several rational fractions a_1/q_1, ..., a_n/q_n with smaller denominators. We show that in the special cases of n=3 and n=4 and…
The relaxed physical factorization (RPF) preconditioner is a recent algorithm allowing for the efficient and robust solution to the block linear systems arising from the three-field displacement-velocity-pressure formulation of coupled…
In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned…
It is well known that liveness properties cannot be proven using standard simulation arguments. This issue has been mitigated by extending standard notions of simulation for transition systems to fairness-preserving simulations for systems…
A mathematical proposition with a trainable pair, operator and quantum circuit, are introduced to approximate functions expressed as cubic Taylor polynomials, numerical simulations illustrate three cases.
We consider the problem of finding approximate analytical solutions for nonlinear equations typical of physics applications. The emphasis is on the modification of the method of Pad\'e approximants that are known to provide the best…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
We perform a systematic comparison of various numerical schemes for the approximation of interface problems. We consider unfitted approaches in view of their application to possibly moving configurations. Particular attention is paid to the…
We consider the question of approximating any real number $\alpha$ by sums of $n$ rational numbers $\frac{a_1}{q_1} + \frac{a_2}{q_2} + ... + \frac{a_n}{q_n}$ with denominators $1 \leq q_1, q_2, ..., q_n \leq N$. This leads to an inquiry on…
We propose a novel extension to symmetrized neural network operators by incorporating fractional and mixed activation functions. This study addresses the limitations of existing models in approximating higher-order smooth functions,…