Related papers: Efficient Interpolation in the Guruswami-Sudan Alg…
The paper presents two algorithms for finding irreducible decomposition of monomial ideals. The first one is recursive, derived from staircase structures of monomial ideals. This algorithm has a good performance for highly non-generic…
The manuscript describes efficient algorithms for the computation of the CUR and ID decompositions. The methods used are based on simple modifications to the classical truncated pivoted QR decomposition, which means that highly optimized…
Richardson extrapolation is a classical technique from numerical analysis that can improve the approximation error of an estimation method by combining linearly several estimates obtained from different values of one of its hyperparameters,…
In this paper, a new algebraic soft-decision decoding algorithm for Reed-Solomon code is presented. It is based on rational interpolation and the interpolation points are constructed by Berlekamp-Messay algorithm. Unlike the traditional…
As a generalization of Hermite interpolation problem, Birkhoff interpolation is an important subject in numerical approximation. This paper generalizes the existing Generalized Recursive Polynomial Interpolation Algorithm (GRPIA) that is…
Compression is a crucial solution for data reduction in modern scientific applications due to the exponential growth of data from simulations, experiments, and observations. Compression with progressive retrieval capability allows users to…
We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the…
Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…
The Numerical Recipes series of books are a useful resource, but all the algorithms they contain cannot be used within open-source projects. In this paper we develop drop-in alternatives to the two algorithms they present for cubic spline…
Using elementary methods, we define and derive a particular weighted average of the trapezoidal and composite trapezoidal rules and show that this approximation, as well as its composite, is straightforward in computation. This…
Image zooming is the process of enlarging the spatial resolution of a given digital image. We present a novel technique that intelligently modifies the classical pixel replication method for zooming. Our method decomposes a given image into…
Multiplication is one of the most important operation in computer arithmetic. Many integer operations such as squaring, division and computing reciprocal require same order of time as multiplication whereas some other operations such as…
In this paper, we suggest a new efficient algorithm in order to compute S-polynomial reduction rapidly in the known algorithm for computing Grobner bases, and compare the complexity with others.
In this paper, we present an iterative soft-decision decoding algorithm for Reed-Solomon codes offering both complexity and performance advantages over previously known decoding algorithms. Our algorithm is a list decoding algorithm which…
We consider model reduction of large-scale multi-input, multi-output (MIMO) systems using tangential interpolation in the frequency domain. Our scheme is related to the recently-developed Adaptive Antoulas--Anderson (AAA) algorithm, which…
Interpolation based image zooming methods provide a high execution speed and low computational complexity. However, the quality of the zoomed images is unsatisfactory in many cases. The main challenge of super- resolution methods is to…
Existing high-performance deep learning models require very intensive computing. For this reason, it is difficult to embed a deep learning model into a system with limited resources. In this paper, we propose the novel idea of the network…
In this paper, we consider signal interpolation of discrete-time signals which are decimated nonuniformly. A conventional interpolation method is based on the sampling theorem, and the resulting system consists of an ideal filter with…
We present algorithms for computing the reduced Gr\"{o}bner basis of the vanishing ideal of a finite set of points in a frame of ideal interpolation. Ideal interpolation is defined by a linear projector whose kernel is a polynomial ideal.…
In this article, we present a fast algorithm performing an instance of the Guruswami-Sudan list decoder for algebraic geometry codes. We show that any such code can be decoded in $\tilde{O}(s^2\ell^{\omega-1}\mu^{\omega-1}(n+g) +…