Upper bounds for the condition numbers of the GCD and the reciprocal GCD matrices in spectral norm

DOI10.1016/j.camwa.2011.11.016zbMath1238.15003OpenAlexW1981107817MaRDI QIDQ418378

Ahmet İpek

Publication date: 28 May 2012

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2011.11.016

zbMATH Keywords

matrix normsEuler's \(\varphi \) functionGCD matrices

Mathematics Subject Classification ID

Matrices of integers (15B36) Conditioning of matrices (15A12) Matrices, determinants in number theory (11C20)

Cites Work

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• A note on a lower bound for the smallest singular value
• A note on the norms of the GCD matrix
• Greatest common divisor matrices
• On GCD and LCM matrices
• On the Bourque-Ligh conjecture of least common multiple matrices
• Matrices associated with classes of arithmetical functions
• Nonsingularity of matrices associated with classes of arithmetical functions on lcm-closed sets
• Arithmetical properties of generalized Ramanujan sums
• Gcd-closed sets and determinants of matrices associated with arithmetical functions
• Determinants of multiplicative Toeplitz matrices
• Power GCD Matrices for a UFD
• A Generalization of Smith's Determinant
• ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF GREATEST COMMON DIVISOR MATRICES
• ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF RECIPROCAL POWER LCM MATRICES

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