Related papers: Recurrence relations and fast algorithms
In this paper we give efficient algorithms for computing second-, third-, and fourth-order linear recurrences. We also present an algorithm scheme for computing terms with the indices $N,\ldots,N+n-1$ of an $n$th-order linear recurrence.…
For a linearly recurrent vector sequence P[n+1] = A(n) * P[n], consider the problem of calculating either the n-th term P[n] or L<=n arbitrary terms P[n_1],...,P[n_L], both for the case of constant coefficients A(n)=A and for a matrix A(n)…
New iterative methods for solving linear equations are presented that are easy to use, generalize good existing methods, and appear to be faster. The new algorithms mix two kinds of linear recurrence formulas. Older methods have either high…
In this paper, we present a new algorithm for computing the linear recurrence relations of multi-dimensional sequences. Existing algorithms for computing these relations arise in computational algebra and include constructing structured…
We consider the problem of developing automated techniques for solving recurrence relations to aid the expected-runtime analysis of programs. Several classical textbook algorithms have quite efficient expected-runtime complexity, whereas…
Computationally efficient classification system architecture is proposed. It utilizes fast tensor-vector multiplication algorithm to apply linear operators upon input signals . The approach is applicable to wide variety of recognition…
We present a simple and fast algorithm for computing the $N$-th term of a given linearly recurrent sequence. Our new algorithm uses $O(\mathsf{M}(d) \log N)$ arithmetic operations, where $d$ is the order of the recurrence, and…
An efficient numerical algorithm for the computation of linking number is presented. The algorithm keep tracks or rounding error so that it can ensure the correctness of the results.
We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…
We consider two kinds of problems: the computation of polynomial and rational solutions of linear recurrences with coefficients that are polynomials with integer coefficients; indefinite and definite summation of sequences that are…
Recurrence equations have played a central role in static cost analysis, where they can be viewed as abstractions of programs and used to infer resource usage information without actually running the programs with concrete data. Such…
Two very fast and simple O(lg n) algorithms for individual Fibonacci numbers are given and compared to competing algorithms. A simple O(lg n) recursion is derived that can also be applied to Lucas. A formula is given to estimate the largest…
In this work we describe a fast and stable algorithm for the computation of the orthogonal moments of an image. Indeed, orthogonal moments are characterized by a high discriminative power, but some of their possible formulations are…
We describe an algorithm that takes as input a complex sequence $(u_n)$ given by a linear recurrence relation with polynomial coefficients along with initial values, and outputs a simple explicit upper bound $(v_n)$ such that $|u_n| \leq…
We study tight bounds and fast algorithms for LCLMs of several linear differential operators with polynomial coefficients. We analyze the arithmetic complexity of existing algorithms for LCLMs, as well as the size of their outputs. We…
We give an algorithm for reversion of formal power series, based on an efficient way to implement the Lagrange inversion formula. Our algorithm requires $O(n^{1/2}(M(n) + MM(n^{1/2})))$ operations where $M(n)$ and $MM(n)$ are the costs of…
A fast simple O(\log n) iteration algorithm for individual Lucas numbers is given. This is faster than using Fibonacci based methods because of the structure of Lucas numbers. Using a sqrt 5 conversion factor on Lucus numbers gives a faster…
We present here a new algorithm for the fast computation of N-point correlation functions in large astronomical data sets. The algorithm is based on kdtrees which are decorated with cached sufficient statistics thus allowing for orders of…
Automatic static cost analysis infers information about the resources used by programs without actually running them with concrete data, and presents such information as functions of input data sizes. Most of the analysis tools for logic…
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…