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Note on dynamic relaxation
Author(s) -
Wood Winifred L.
Publication year - 1971
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620030115
Subject(s) - mathematics , spectral radius , relaxation (psychology) , chebyshev filter , mathematical analysis , matrix (chemical analysis) , moduli , convergence (economics) , degenerate energy levels , rate of convergence , upper and lower bounds , set (abstract data type) , eigenvalues and eigenvectors , physics , computer science , psychology , social psychology , channel (broadcasting) , materials science , computer network , quantum mechanics , economics , composite material , programming language , economic growth
The Dynamic Relaxation ( DR ) method of solving a set of simultaneous linear equations requires an estimate of the spectral radius of the matrix. Dividing each equation by the corresponding row sum of moduli of the elements of the matrix gives a convenient upper bound of unity to this. This note shows that the DR method then gives a faster asymptotic rate of the convergence than the degenerate Chebyshev method which it closely resembles.