A parallel algorithm for evaluating general linear recurrence equations

1996 ◽  
Vol 15 (4) ◽  
pp. 481-504
Author(s):  
Mi Lu ◽  
Xiangzhen Qiao ◽  
Guanrong Chen
Keyword(s):  
Parallel Algorithm ◽  
General Linear ◽  
Linear Recurrence ◽  
Recurrence Equations

scholarly journals Parallel Tiled Code for Computing General Linear Recurrence Equations

Electronics ◽  
2021 ◽  
Vol 10 (17) ◽  
pp. 2050
Author(s):  
Włodzimierz Bielecki ◽  
Piotr Błaszyński
Keyword(s):  
Performance Improvement ◽  
General Linear ◽  
Multidimensional Data ◽  
Linear Recurrence ◽  
Data Dependencies ◽  
Recurrence Equations ◽  
Code Performance ◽  
Parallel Code ◽  
Linear Recursion

In this article, we present a technique that allows us to generate parallel tiled code to calculate general linear recursion equations (GLRE). That code deals with multidimensional data and it is computing-intensive. We demonstrate that data dependencies available in an original code computing GLREs do not allow us to generate any parallel code because there is only one solution to the time partition constraints built for that program. We show how to transform the original code to another one that exposes dependencies such that there are two linear distinct solutions to the time partition restrictions derived from these dependencies. This allows us to generate parallel 2D tiled code computing GLREs. The wavefront technique is used to achieve parallelism, and the generated code conforms to the OpenMP C/C++ standard. The experiments that we conducted with the resulting parallel 2D tiled code show that this code is much more efficient than the original serial code computing GLREs. Code performance improvement is achieved by allowing parallelism and better locality of the target code.

scholarly journals General Linear Recurrence Sequences and Their Convolution Formulas

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 132 ◽  
Author(s):  
Paolo Emilio Ricci ◽  
Pierpaolo Natalini
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Second Order ◽  
General Linear ◽  
Linear Recurrence ◽  
Order Linear ◽  
Matrix Polynomials ◽  
Recurrence Sequences ◽  
Straightforward Extension

We extend a technique recently introduced by Chen Zhuoyu and Qi Lan in order to find convolution formulas for second order linear recurrence polynomials generated by 1 1 + a t + b t 2 x . The case of generating functions containing parameters, even in the numerator is considered. Convolution formulas and general recurrence relations are derived. Many illustrative examples and a straightforward extension to the case of matrix polynomials are shown.

scholarly journals m-Fold Hypergeometric Solutions of Linear Recurrence Equations Revisited

2012 ◽  
Vol 6 (1) ◽  
pp. 61-77 ◽  
Author(s):  
Peter Horn ◽  
Wolfram Koepf ◽  
Torsten Sprenger
Keyword(s):  
Linear Recurrence ◽  
Recurrence Equations ◽  
Hypergeometric Solutions

scholarly journals Analytical calculation of the deflection of an externally statically indeterminate lattice truss

2019 ◽  
Vol 265 ◽  
pp. 05027
Author(s):  
Mikhail Kirsanov ◽  
Evgeny Komerzan ◽  
Olesya Sviridenko
Keyword(s):  
Arbitrary Number ◽  
Analytical Calculation ◽  
Linear Recurrence ◽  
System Of Equations ◽  
Induction Method ◽  
Particular Solutions ◽  
Recurrence Equations ◽  
Nonmonotonic Character

A scheme of a statically definable truss with additional supports is proposed. Derive formulas for the dependence of the deflection of the truss against the number of panels for three types of symmetrical loads. It is shown that for definite numbers of panels the determinant of the system of equations for the equilibrium of nodes degenerates. This indicates an instant changeability of the structure. To generalize particular solutions to an arbitrary number of panels, the induction method is applied. For this purpose, in the computer mathematics system Maple linear recurrence equations are constructed for the terms of a sequence of coefficients from individual solutions. The graphs of the dependences obtained indicate a nonmonotonic character of the solutions found and the possibility of optimizing the design by choosing the number of panels.

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