Related papers: A new multidimensional slow continued fraction alg…
The fast multipole method (FMM) performs fast approximate kernel summation to a specified tolerance $\epsilon$ by using a hierarchical division of the domain, which groups source and receiver points into regions that satisfy local…
A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…
In this partly expository paper, we discuss three results. (1) That the two-sided continued fraction of the normalized square root (an important part of the SQUFOF algorithm) has several very attractive properties - periodicity, a symmetry…
This paper investigates integer multiplication of continued fractions using geometric structures. In particular, this paper shows that integer multiplication of a continued fraction can be represented by replacing one triangulation of an…
We present a new algorithm for the 2D Sliding Window Discrete Fourier Transform (SWDFT). Our algorithm avoids repeating calculations in overlapping windows by storing them in a tree data-structure based on the ideas of the Cooley- Tukey…
The problem of developing an arithmetic for continued fractions (in order to perform, e.g., sums and products) does not have a straightforward solution and has been addressed by several authors. In 1972, Gosper provided an algorithm to…
This paper presents a fast "two-dimensional Fourier Continuation" (2D-FC) method for the construction of biperiodic extensions of smooth, non-periodic functions defined over general two-dimensional (2D) domains, including domains with…
A fully discrete finite element method, based on a new weak formulation and a new time-stepping scheme, is proposed for the surface diffusion flow of closed curves in the two-dimensional plane. It is proved that the proposed method can…
We present several continued fraction algorithms, each of which gives an eventually periodic expansion for every quadratic element of ${\mathbb Q}_p$ over ${\mathbb Q}$ and gives a finite expansion for every rational number. We also give,…
We set new speed records for multiplying long polynomials over finite fields of characteristic two. Our multiplication algorithm is based on an additive FFT (Fast Fourier Transform) by Lin, Chung, and Huang in 2014 comparing to previously…
The disadvantage of `traditional' multidimensional continued fraction algorithms is that it is not known whether they provide simultaneous rational approximations for generic vectors. Following ideas of Dani, Lagarias and Kleinbock-Margulis…
In this paper we develop a new geometric approach to subtractive continued fraction algorithms in high dimensions. We adapt a version of Farey summation to the geometric techniques proposed by F. Klein in 1895. More specifically we…
We present a novel linear subdivision scheme for face-based tangent directional fields on triangle meshes. Our subdivision scheme is based on a novel coordinate-free representation of directional fields as halfedge-based scalar quantities,…
As a new type of series expansion, the so-called one-dimensional adaptive Fourier decomposition (AFD) and its variations (1D-AFDs) have effective applications in signal analysis and system identification. The 1D-AFDs have considerable…
The Fast Reciprocal Square Root Algorithm is a well-established approximation technique consisting of two stages: first, a coarse approximation is obtained by manipulating the bit pattern of the floating point argument using integer…
We first survey the current state of the art concerning the dynamical properties of multidimensional continued fraction algorithms defined dynamically as piecewise fractional maps and compare them with algorithms based on lattice reduction.…
We propose and study a generalized continued fraction algorithm that can be executed in an arbitrary imaginary quadratic field, the novelty being a non-restriction to the five Euclidean cases. Many hallmark properties of classical continued…
Multidimensional continued fractions (MCFs) were introduced by Jacobi and Perron in order to generalize the classical continued fractions. In this paper, we propose an introductive fundamental study about MCFs in the field of the $p$--adic…
We provide a framework for the design and analysis of dynamic programming algorithms for surface-embedded graphs on n vertices and branchwidth at most k. Our technique applies to general families of problems where standard dynamic…
Point containment queries on trimmed surfaces are fundamental to CAD modeling, solid geometry processing, and surface tessellation. Existing approaches such as ray casting and generalized winding numbers often face limitations in robustness…