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Fault-tolerant quantum computing requires classical hardware to perform the decoding necessary for error correction. The Union-Find decoder is one of the best candidates for this. It has remarkably organic characteristics, involving the…

Quantum Physics · Physics 2023-11-15 Tim Chan , Simon C. Benjamin

We propose a kernel compression method for solving Distributed-Order (DO) Fractional Partial Differential Equations (DOFPDEs) at the cost of solving corresponding local-in-time PDEs. The key concepts are (1) discretization of the integral…

Numerical Analysis · Mathematics 2025-08-20 Jonas Beddrich , Barbara Wohlmuth

It's well know that Radial Basis Function approximants suffers of bad conditioning if the simple basis of translates is used. A recent work of M.Pazouki and R.Schaback gives a quite general way to build stable, orthonormal bases for the…

Numerical Analysis · Mathematics 2018-10-09 Gabriele Santin

The aim of this paper is to present a first evaluation of a dynamic partition strategy associated to the recently proposed asynchronous distributed computation scheme based on the D-iteration approach. The D-iteration is a fluid diffusion…

Distributed, Parallel, and Cluster Computing · Computer Science 2012-03-13 Dohy Hong

The nonuniform fast Fourier transform (NUFFT) enables spectral methods for problems with irregularly spaced samples, with applications in medical imaging, molecular dynamics, and kinetic plasma simulations. Existing implementations are…

Computational Engineering, Finance, and Science · Computer Science 2026-05-12 Paul Fischill , Andreas Adelmann , Sriramkrishnan Muralikrishnan

In this paper, we propose an iterative algorithm using polar decomposition to approximate a channel characterized by a single unitary matrix based on input-output quantum state pairs. In limited data, we state and prove that the optimal…

Numerical Analysis · Mathematics 2025-06-27 Matthew M. Lin , Hao-Wei Huang , Bing-Ze Lu

An important component of a number of computational modeling algorithms is an interpolation method that preserves the positivity of the function being interpolated. This report describes the numerical testing of a new positivity-preserving…

Numerical Analysis · Mathematics 2022-06-17 T. A. J. Ouermi , Robert M. Kirby , Martin Berzins

A function approximation method is developed that aims to approximate a function in a small neighborhood of a state that travels within a compact set. The development is based on the theory of universal reproducing kernel Hilbert spaces…

Optimization and Control · Mathematics 2021-07-07 Joel A. Rosenfeld , Rushikesh Kamalapurkar , Warren E. Dixon

The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using…

Optimization and Control · Mathematics 2017-11-10 Guillermo Gallego , Daniel Berjón , Narciso García

Radial basis functions (RBFs) play an important role in function interpolation, in particular in an arbitrary set of interpolation nodes. The accuracy of the interpolation depends on a parameter called the shape parameter. There are many…

Numerical Analysis · Mathematics 2025-08-27 Maria Han Veiga , Faezeh Nassajian Mojarrad , Fatemeh Nassajian Mojarrad

W projection is a commonly-used approach to allow interferometric imaging to be accelerated by Fast Fourier Transforms (FFTs), but it can require a huge amount of storage for convolution kernels. The kernels are not separable, but we show…

Instrumentation and Methods for Astrophysics · Physics 2016-01-27 Bruce Merry

Discretizing an analytic function on a uniform real-space grid is often done via a straightforward collocation method. This is ubiquitous in all areas of computational physics and quantum chemistry. An example in Density Functional Theory…

Computational Physics · Physics 2016-01-20 Luigi Genovese , Thierry Deutsch

We study algorithms to estimate geometric properties of raw point cloud data through implicit surface representations. Given that any level-set function with a constant level set corresponding to the surface can be used for such…

Numerical Analysis · Mathematics 2026-04-02 Alex Shiu Lun Chu , Leevan Ling , Ka Chun Cheung

We present a subsampling strategy for the offline stage of the Reduced Basis Method. The approach is aimed at bringing down the considerable offline costs associated with using a finely-sampled training set. The proposed algorithm exploits…

Numerical Analysis · Mathematics 2023-01-24 Sridhar Chellappa , Lihong Feng , Peter Benner

In this work, we propose an approach to perform non-uniform image interpolation based on a Gaussian Mixture Model. Traditional image interpolation methods, like nearest neighbor, bilinear, Hamming, Lanczos, etc. assume that the coordinates…

Computer Vision and Pattern Recognition · Computer Science 2020-12-25 Ivan Skorokhodov

We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and…

Data Structures and Algorithms · Computer Science 2021-09-13 Kaan Gokcesu , Hakan Gokcesu

One approach to achieving correct finite element assembly is to ensure that the local orientation of facets relative to each cell in the mesh is consistent with the global orientation of that facet. Rognes et al. have shown how to achieve…

Mathematical Software · Computer Science 2016-11-17 Miklós Homolya , David A. Ham

We present GridFF, an efficient method for simulating molecules on rigid substrates, derived from techniques used in protein-ligand docking in biochemistry. By projecting molecule-substrate interactions onto precomputed spatial grids with…

Chemical Physics · Physics 2025-08-22 Indranil Mal , Milan Kočí , Paolo Nicolini , Prokop Hapala

We investigate fusing several unreliable computational units that perform the same task. We model an unreliable computational outcome as an additive perturbation to its error-free result in terms of its fidelity and cost. We analyze…

Performance · Computer Science 2017-05-23 Mehmet A. Donmez , Maxim Raginsky , Andrew C. Singer , Lav R. Varshney

The notion of well-separated sets is crucial in fast multipole methods as the main idea is to approximate the interaction between such sets via cluster expansions. We revisit the one-parameter multipole acceptance criterion in a general…

Numerical Analysis · Mathematics 2011-08-11 Stefan Engblom