Reducing rational polynomial: a proposition of a strategy to deal with floating point numbers using singular value decomposition

2022 ◽  
Author(s):  
Ahmad Deeb ◽  
Rafik Belarbi
Keyword(s):  
Singular Value Decomposition ◽  
Singular Value ◽  
Floating Point ◽  
Rational Polynomial ◽  
Value Decomposition ◽  
Floating Point Numbers

scholarly journals Reducing Rational Polynomial: A Proposition of a Strategy to Deal With Floating Points Numbers Using SVD

2021 ◽  
Author(s):  
Ahmad DEEB ◽  
Rafik Belarbi
Keyword(s):  
Small Degree ◽  
Singular Value ◽  
Floating Point ◽  
Floating Point Arithmetic ◽  
Rational Polynomial ◽  
New Strategy ◽  
Value Decomposition ◽  
Time Accuracy ◽  
Greatest Common Divisors ◽  
Point Arithmetic

Abstract In this article, we present a new strategy to reduce rational polynomial based on the kernel of a linear map defined by the matrix's Sylvester. The strategy does not hold the computation of the Greatest common divisors (GCD) of two polynomials, as other algorithms do, but produce the reduced fraction directly. This strategy was inspired when we consider elements of Padé approximant as a basis is the Proper Generalised Decomposition for solving Partial Differential equation. The algorithm can use the Singular value decomposition technique when dealing with a polynomial with floating-point arithmetic. We compare it with Brown's algorithm in two wedges: multiplication for finite fields and large integers. Results are shown in term of time computation and robustness. The proposed algorithm shows that the time accuracy of computing the reduced fractional is at the same order as the Brown algorithm for finite field and large integers when the GCD of both polynomials has a small degree and an improving when the GCD's degree increase with the degree of polynomials. Also, robustness is more dynamic when arithmetic with the floating-point operation.

Improving TF-IDF with Singular Value Decomposition (SVD) for Feature Extraction on Twitter

2017 ◽  
Author(s):  
Ammar Ismael Kadhim ◽  
Yu-N Cheah ◽  
Inaam Abbas Hieder ◽  
Rawaa Ahmed Ali
Keyword(s):  
Feature Extraction ◽  
Singular Value Decomposition ◽  
Singular Value ◽  
Value Decomposition

Multi-scale singular value decomposition polarization image fusion defogging algorithm and experiment

2020 ◽  
Vol 13 (6) ◽  
pp. 1-10
Author(s):  
ZHOU Wen-zhou ◽  
◽  
FAN Chen ◽  
HU Xiao-ping ◽  
HE Xiao-feng ◽  
...  
Keyword(s):  
Singular Value Decomposition ◽  
Image Fusion ◽  
Singular Value ◽  
Multi Scale ◽  
Polarization Image ◽  
Value Decomposition
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