Related papers: Fast Hermite interpolation and evaluation over fin…
A new algorithm to approximate Hermitian matrices by positive semidefinite Hermitian matrices based on modified Cholesky decompositions is presented. In contrast to existing algorithms, this algorithm allows to specify bounds on the…
Multipoint evaluation is the computational task of evaluating a polynomial given as a list of coefficients at a given set of inputs. And while \emph{nearly linear time} algorithms have been known for the univariate instance of multipoint…
This article presents novel proof methods for estimating interpolation errors, predicated on the understanding that one has already studied foundational error analysis using the finite element method.
We consider the problem of identity testing and recovering (that is, interpolating) of a "hidden" monic polynomials $f$, given an oracle access to $f(x)^e$ for $x\in\mathbb F_q$, where $\mathbb F_q$ is the finite field of $q$ elements and…
Video frame interpolation is an important low-level vision task, which can increase frame rate for more fluent visual experience. Existing methods have achieved great success by employing advanced motion models and synthesis networks.…
A new algorithm for one-dimensional minimization is described in detail and the results of some tests on practical cases are reported and illustrated. The method requires only punctual computation of the function, and is suitable to be…
In this study, a new $\Delta$-evaluation method is introduced for solving a column permutation problem defined on a sparse binary matrix with the consecutive ones property. This problem models various $\mathcal{NP}$-hard problems in graph…
This paper develops a unified theoretical framework for constructing B-spline basis function spaces with structural equivalence to finite element spaces. The theory rigorously establishes that these bases emerge as explicit linear…
I discuss a simple numerical algorithm for the direct evaluation of multiple Grassmann integrals. The approach is exact, suffers no Fermion sign problems, and allows arbitrarily complicated interactions. Memory requirements grow…
A Fast algorithm for the Discrete Hartley Transform (DHT) is presented, which resembles radix-2 fast Fourier Transform (FFT). Although fast DHTs are already known, this new approach bring some light about the deep relationship between fast…
Most deep learning methods for video frame interpolation consist of three main components: feature extraction, motion estimation, and image synthesis. Existing approaches are mainly distinguishable in terms of how these modules are…
We derive a Fast Multipole Method (FMM) where a low-rank approximation of the kernel is obtained using the Empirical Interpolation Method (EIM). Contrary to classical interpolation-based FMM, where the interpolation points and basis are…
The application of error-free transformation (EFT) is recently being developed to solve ill-conditioned problems. It can reduce the number of arithmetic operations required, compared with multiple precision arithmetic, and also be applied…
This paper studies path synthesis for nonholonomic mobile robots moving in two-dimensional space. We first address the problem of interpolating paths expressed as sequences of straight line segments, such as those produced by some planning…
New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The…
In practice, deep neural networks are often able to easily interpolate their training data. To understand this phenomenon, many works have aimed to quantify the memorization capacity of a neural network architecture: the largest number of…
We study the interpolation analogue of the Hermite-Pad\'e type I approximation problem. We provide its determinant solution and we write down the corresponding integrable discrete system as an admissible reduction of Hirota's discrete…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
In this paper we propose a global optimization-based approach to jointly matching a set of images. The estimated correspondences simultaneously maximize pairwise feature affinities and cycle consistency across multiple images. Unlike…
The effective formulas reducing the two-dimensional Hermite polynomials to the classical (one-dimensional) orthogonal polynomials are given. New one-parameter generating functions for these polynomials are derived. Asymptotical formulas for…