Paper Info
Title
Upper bounds for the condition numbers of the GCD and the reciprocal GCD matrices in spectral norm
Abstract
Let S={x"1,...,x"n} be a set of n distinct positive integers. The nxn matrix having the greatest common divisor (x"i,x"j) of x"i and x"j as its i,j-entry is called the greatest common divisor (GCD) matrix defined on S, denoted by ((x"i,x"j)), or abbreviated as (S). The nxn matrix (S^-^1)=(g"i"j), where g"i"j=1(x"i,x"j), is called the reciprocal greatest common divisor (GCD) matrix on S. In this paper, we present upper bounds for the spectral condition numbers of the reciprocal GCD matrix (S^-^1) and the GCD matrix (S) defined on S={1,2,...,n}, with n=2, as a function of Euler's @f function and n.
Year
DOI
Venue
2012
10.1016/j.camwa.2011.11.016
Computers & Mathematics with Applications
Keywords
Field
DocType
spectral condition number,reciprocal greatest common divisor,reciprocal gcd matrix,n distinct positive integer,gcd matrix,spectral norm,greatest common divisor,upper bound,nxn matrix,matrix norms
Integer,Discrete mathematics,Reciprocal,Matrix (mathematics),Matrix norm,Euler's formula,Greatest common divisor,Mathematics
Journal
Volume
Issue
ISSN
63
3
0898-1221
Citations 
PageRank 
References 
0
0.34
0
Authors
1
Name
Order
Citations
PageRank
Ahmet Ipek171.82