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On the convergence theory of double K -weak splittings of type II

Vaibhav Shekhar, Nachiketa Mishra, Debasisha Mishra (2022)

Applications of Mathematics

Recently, Wang (2017) has introduced the K -nonnegative double splitting using the notion of matrices that leave a cone K n invariant and studied its convergence theory by generalizing the corresponding results for the nonnegative double splitting by Song and Song (2011). However, the convergence theory for K -weak regular and K -nonnegative double splittings of type II is not yet studied. In this article, we first introduce this class of splittings and then discuss the convergence theory for these sub-classes...

On the divisibility of power LCM matrices by power GCD matrices

Jian Rong Zhao, Shaofang Hong, Qunying Liao, Kar-Ping Shum (2007)

Czechoslovak Mathematical Journal

Let S = { x 1 , , x n } be a set of n distinct positive integers and e 1 an integer. Denote the n × n power GCD (resp. power LCM) matrix on S having the e -th power of the greatest common divisor ( x i , x j ) (resp. the e -th power of the least common multiple [ x i , x j ] ) as the ( i , j ) -entry of the matrix by ( ( x i , x j ) e ) (resp. ( [ x i , x j ] e ) ) . We call the set S an odd gcd closed (resp. odd lcm closed) set if every element in S is an odd number and ( x i , x j ) S (resp. [ x i , x j ] S ) for all 1 i , j n . In studying the divisibility of the power LCM and power GCD matrices, Hong conjectured in 2004 that...

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