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Object completion networks typically produce static Signed Distance Fields (SDFs) that faithfully reconstruct geometry but cannot be rescaled or deformed without introducing structural distortions. This limitation restricts their use in…
We present a parallel version of the well-known Split-Step Fourier method (SSF) for solving the Nonlinear Schr\"odinger equation, a mathematical model describing wave packet propagation in fiber optic lines. The algorithm is implemented…
A novel parallel algorithm for matrix multiplication is presented. The hyper-systolic algorithm makes use of a one-dimensional processor abstraction. The procedure can be implemented on all types of parallel systems. It can handle…
This paper describes a novel approach to neighbour-finding in Smoothed Particle Hydrodynamics (SPH) simulations with large dynamic range in smoothing length. This approach is based on hierarchical cell decompositions, sorted interactions,…
Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…
We introduce two efficient algorithms for computing the partial Fourier transforms in one and two dimensions. Our study is motivated by the wave extrapolation procedure in reflection seismology. In both algorithms, the main idea is to…
This paper proposes a new second-order symmetric algorithm for solving decoupled forward-backward stochastic differential equations. Inspired by the alternating direction implicit splitting method for partial differential equations, we…
We introduce a fast algorithm for computing sparse Fourier transforms supported on smooth curves or surfaces. This problem appear naturally in several important problems in wave scattering and reflection seismology. The main observation is…
Signed distance fields (SDFs) are a widely used implicit surface representation, with broad applications in computer graphics, computer vision, and applied mathematics. To reconstruct an explicit triangle mesh surface corresponding to an…
We describe geometric algorithms that generalize the classical continued fraction algorithm for the torus to all translation surfaces in hyperelliptic components of translation surfaces. We show that these algorithms produce all saddle…
Multi-block separable convex problems recently received considerable attention. This class of optimization problems minimizes a separable convex objective function with linear constraints. The algorithmic challenges come from the fact that…
We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by…
This article introduces a functional method for lower-dimensional smooth representations in terms of time-varying dissimilarities. The method incorporates dissimilarity representation in multidimensional scaling and smoothness approach of…
Fourier ptychographic microscopy enables gigapixel-scale imaging, with both large field-of-view and high resolution. Using a set of low-resolution images that are recorded under varying illumination angles, the goal is to computationally…
Edge-preserving smoothing is a fundamental procedure for many computer vision and graphic applications. This can be achieved with either local methods or global methods. In most cases, global methods can yield superior performance over…
In this article we propose a new adaptive numerical quadrature procedure which includes both local subdivision of the integration domain, as well as local variation of the number of quadrature points employed on each subinterval. In this…
We implement an Augmented Lagrangian method to minimize a constrained least-squares cost function designed to find polyadic decompositions of the matrix multiplication tensor. We use this method to obtain new discrete decompositions and…
We describe an adaptive greedy algorithm for Thiele continued-fraction approximation of a function defined on a continuum domain in the complex plane. The algorithm iteratively selects interpolation nodes from an adaptively refined set of…
In this paper we consider the numerical solution of Fractional Differential Equations by means of $m$-step recursions. The construction of such formulas can be obtained in many ways. Here we study a technique based on the rational…
This paper investigates the efficient solution of penalized quadratic regressions in high-dimensional settings. A novel and efficient algorithm for ridge-penalized quadratic regression is proposed, leveraging the matrix structures of the…