کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
471618 698651 2012 7 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Upper bounds for the condition numbers of the GCD and the reciprocal GCD matrices in spectral norm
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر علوم کامپیوتر (عمومی)
پیش نمایش صفحه اول مقاله
Upper bounds for the condition numbers of the GCD and the reciprocal GCD matrices in spectral norm
چکیده انگلیسی

Let S={x1,…,xn}S={x1,…,xn} be a set of nn distinct positive integers. The n×nn×n matrix having the greatest common divisor (xi,xj)(xi,xj) of xixi and xjxj as its i,ji,j-entry is called the greatest common divisor (GCD) matrix defined on SS, denoted by ((xi,xj))((xi,xj)), or abbreviated as (S)(S). The n×nn×n matrix (S−1)=(gij)(S−1)=(gij), where gij=1(xi,xj), is called the reciprocal greatest common divisor (GCD) matrix on SS. In this paper, we present upper bounds for the spectral condition numbers of the reciprocal GCD matrix (S−1)(S−1) and the GCD matrix (S)(S) defined on S={1,2,…,n}S={1,2,…,n}, with n≥2n≥2, as a function of Euler’s ϕϕ function and nn.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computers & Mathematics with Applications - Volume 63, Issue 3, February 2012, Pages 645–651
نویسندگان
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