Galerkin's method and stability

摘要

AbstractApproximation 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 mentio