Chebyshev
No mentions found
This entity hasn't been tracked yet, or Iris is still building its knowledge base.
Related Articles from SNS
Chebyshev Policies and the Mountain Car Problem: Reinforcement Learning for Low-Dimensional Control Tasks
arXiv:2605.22305v2 Announce Type: replace Abstract: We analytically solve the Mountain Car problem, a canonical benchmark in RL, and derive an optimal control solution, closing a gap after 36 years. This enables us to reveal two surprising insights: The optimal control is quite simple, yet modern RL agents display a large gap to optimality. Motivated by the analysis of the optimal control, we introduce Chebyshev policies as a universal (i.e. dense) class of RL policies from first principles.
A novel Chebyshev collocation method for elliptic -type differential equations with degenerate coefficient
new Abstract: A novel collocation scheme is presented for elliptic-type differential equations with degenerate coefficients and homogeneous Dirichlet boundary conditions. The use of weighted orthogonal Chebyshev polynomials for the basis functions leads to stiffness matrices with sparse structure, enabling efficient direct calculations. By an orthogonal projection, rigorous analyses are devoted to deriving a-priori error estimates of spectral accuracy in two norms.
Fractional calculus via variable-transform-based spectral approximations
Announce Type: replace Abstract: We present a novel and unifying framework for constructing spectral approximations to fractional integral operators. These spectral approximations are based on transplanted Chebyshev polynomials, which are obtained by composing Chebyshev polynomials with a variable transform. When an algebraic transform is used, the framework produces spectral approximations based on Jacobi fractional polynomials.
Stochastic Density Functional Theory Through the Lens of Multilevel Monte Carlo Method
arXiv:2512.04860v3 Announce Type: replace Abstract: The stochastic density functional theory (sDFT) has exhibited advantages over the standard Kohn-Sham DFT method and has become an attractive approach for large-scale electronic structure calculations. The sDFT method avoids the expensive matrix diagonalization by introducing a set of random orbitals and approximating the density matrix via Chebyshev expansion of a matrix-valued function. In this work, we study the sDFT with a plane-wave...
Comparison of the potential energy for different equilibrium configurations of symmetric and asymmetric floating drops
arXiv:2602.10120v2 Announce Type: replace-cross Abstract: We provide a numerical method for computing solutions to a free boundary problem arising from the equilibrium state of a floating drop. This numerical method is based on a Newton's method for the underlying nonlinear boundary value problems, and at each iterative step a Chebyshev spectral collocation method is employed. The problems considered here are those that can be described by using generating curves, and include problems in...
Comparison of the potential energy for different equilibrium configurations of symmetric and asymmetric floating drops
arXiv:2602.10120v2 Announce Type: replace Abstract: We provide a numerical method for computing solutions to a free boundary problem arising from the equilibrium state of a floating drop. This numerical method is based on a Newton's method for the underlying nonlinear boundary value problems, and at each iterative step a Chebyshev spectral collocation method is employed. The problems considered here are those that can be described by using generating curves, and include problems in...
Missing Links in Public Email and Covert Networks: A Comparative Evaluation of Link Prediction, Hyperlink Prediction, and ERGM Estimation
arXiv:2605.22606v2 Announce Type: replace Abstract: We study missing-link inference in partially observed networks by systematically comparing dyadic link prediction (LP) with hyperlink prediction (HP) and an estimation-based ERGM comparator. LP serves as the primary baseline, using classical heuristics computed on the observed graph. HP extends this framework by scoring candidate higher-order structures (cliques) via lifted dyadic scores and via the CHEbyshev Spectral HyperlInk pREdictor...
On the sharp linear convergence rate of the circumcentered--reflection method on subspaces
arXiv:2606.07888v1 Announce Type: cross Abstract: For two subspaces $U,V\subseteq\RR^n$, the circumcentered--reflection method (CRM) of Behling, Bello-Cruz, and Santos~\cite{BBS2018} computes the projection onto $U\cap V$ using only the reflections across $U$ and $V$, with known linear-convergence rate $c_F$, the cosine of the Friedrichs angle. We prove that, when CRM is initialized in $V$, it contracts at the strictly smaller rate...
Data-Driven Spectral Prediction for Accelerating Large-Scale Electronic Structure Calculations
arXiv:2606.00401v1 Announce Type: cross Abstract: Simulating large molecular systems comprising thousands of atoms requires highly scalable methodologies. While modern Density Functional Theory (DFT) codes exhibit linear scaling, solving the associated large, sparse generalized eigenproblems remains a critical computational bottleneck on exascale architectures. In the context of the LimitX project, we propose a data-driven framework to accelerate these calculations.
Gate the Filter, Not the Message: Node-Channel Mixtures for Pre-Propagation GNNs
arXiv:2606.01660v1 Announce Type: new Abstract: Pre-propagation graph neural networks (PPGNNs) push all graph-dependent computation into a preprocessing step and train only on the resulting dense hop features, which makes them highly scalable. A puzzle in this regime is that more complex hop aggregators do not reliably outperform simpler ones: on many benchmarks, a plain MLP-based aggregator matches or beats hop-attention variants. We revisit this behavior from a graph-filter perspective.