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Galerkin's method and stability
Author(s) -
Jones D. S.
Publication year - 1980
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670020308
Subject(s) - mathematics , galerkin method , eigenvalues and eigenvectors , bounded function , stability (learning theory) , convergence (economics) , computation , extension (predicate logic) , mathematical analysis , finite element method , algorithm , computer science , physics , quantum mechanics , machine learning , economics , thermodynamics , programming language , economic growth
Approximation in least squares by Galerkin's method leads to a consideration of strongly minimal systems. Theorems are derived which permit the recognition of systems which are not strongly minimal from the characteristics of the elements themselves. Normalised systems cannot be strongly minimal without their eigenvalues being bounded above. Speared systems, which have desirable properties, are introduced and their main features determined. Convergence earmarks and error bounds are exposed. A new definition of stability, which is self‐checking in a computation, is suggested and its attributes delineated. The extension of the theory to equations involving positive‐definite operators is mentioned.