Related papers: A symbol based analysis for multigrid methods for …
We present a hierarchical neuro-symbolic control framework that tightly couples a classical symbolic planner with a transformer-based policy to address long-horizon decision-making under uncertainty. At the high level, the planner assembles…
We initiate a systematic framework for the analysis of analytic properties of finite Feynman integrals that are multiple polylogarithms. Based on the Feynman parameter representation in complex projective space, we make a complete…
We introduce a machine-learning framework based on symbolic regression to extract the full symbol alphabet of multi-loop Feynman integrals. By targeting the analytic structure rather than reduction, the method is broadly applicable and…
Fractional diffusion equations (FDEs) are a mathematical tool used for describing some special diffusion phenomena arising in many different applications like porous media and computational finance. In this paper, we focus on a…
Block-oriented nonlinear models are popular in nonlinear modeling because of their advantages to be quite simple to understand and easy to use. To increase the flexibility of single branch block-oriented models, such as Hammerstein, Wiener,…
The aim of this paper is to develop an algebraic multigrid method to solve eigenvalue problems based on the combination of the multilevel correction scheme and the algebraic multigrid method for linear equations. Our approach uses the…
Block-structured problems are central to advances in numerical optimization and machine learning. This paper provides the formalization of convergence analysis for two pivotal algorithms in such settings: the block coordinate descent (BCD)…
In this note we discuss an open problem whether a truncated Toeplitz operator on a model space can be hypercyclic. We compute point spectrum and eigenfunctions for a class of truncated Toeplitz operators with polynomial analytic and…
This study considers the Block-Toeplitz structural properties inherent in traditional multichannel forward model matrices, using Full Matrix Capture (FMC) in ultrasonic testing as a case study. We propose an analytical convolutional forward…
We analyze a three-dimensional discontinuous piecewise linear system \(Z=(X,Y)\) whose switching manifold \(\Sigma\) contains visible-visible two-fold intersection lines. Assuming that the matrices \(DX\) and \(DY\) each have one nonzero…
In this paper we consider a class of unbounded Toeplitz operators with rational matrix symbols that have poles on the unit circle and employ state space realization techniques from linear systems theory, as used in our earlier analysis in…
It is shown how various ideas that are well established for the solution of Poisson's equation using plane wave and multigrid methods can be combined with wavelet concepts. The combination of wavelet concepts and multigrid techniques turns…
The solution of parameter-dependent linear systems, by classical methods, leads to an arithmetic effort that grows exponentially in the number of parameters. This renders the multigrid method, which has a well understood convergence theory,…
A possible solution of the notorious sign problem preventing direct Monte Carlo calculations for systems with non-zero chemical potential is to deform the integration region in the complex plane to a Lefschetz thimble. We investigate this…
The cyclic reduction (CR) algorithm is an efficient method for solving quadratic matrix equations that arise in quasi-birth-death (QBD) stochastic processes. However, its convergence is not guaranteed when the associated matrix polynomial…
In some real world situations, linear models are not sufficient to represent accurately complex relations between input variables and output variables of a studied system. Multilayer Perceptrons are one of the most successful non-linear…
In this paper, we study the hardness of solving graph-structured linear systems with coefficients over a finite field $\mathbb{Z}_p$ and over a polynomial ring $\mathbb{F}[x_1,\ldots,x_t]$. We reduce solving general linear systems in…
We construct multigrid methods for an elliptic distributed optimal control problem that are robust with respect to a regularization parameter. We prove the uniform convergence of the $W$-cycle algorithm and demonstrate the performance of…
The spectral symbols are useful tools to analyse the eigenvalue distribution when dealing with high dimensional linear systems. Given a matrix sequence with an asymptotic symbol, the last one depends only on the spectra of the individual…
In this study, we address the challenge of solving elliptic equations with quasiperiodic coefficients. To achieve accurate and efficient computation, we introduce the projection method, which enables the embedding of quasiperiodic systems…