Approximation Methods in Functional Analysis: Lectures Given in 1959 at the California Institute of Technology, Forming Part of the Course Advanced Topics in Numerical Analysis |
Contents
METRIC SPACES 1 Sci Tech | 6 |
A SIMPLE PRACTICAL METHOD AND A COMPACT COMPUTING SCHEME FOR THE | 12 |
ON THE METHOD OF ORTHOGONAL PROJECTION | 19 |
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Acad additive and homogeneous adjoint apply approximate solutions b₁ Banach spaces best successive approximation conjugate gradient method contraction mapping Corollary cosine equation critical value defined by process denotes differential P'(x eigenvector equations in Hilbert error estimate exists following conditions following theorem formulae 16 ɣki Hence Hilbert space hyperpower initial approximation inverse iterative method iterative process least squares Lemma Let us assume linear bounded operator linear equation linear operator linearly independent majorant equation matrix matrix calculus maximum eigenvalues method of least method of steepest metric space minimum Newton's method non-linear functional equation non-singular norm obtain operator equations operator in Hilbert orthogonal projection paper 18 Polon positive definite positive number rate of convergence Remark replaced satisfies condition satisfies the condition self-adjoint and positive sequence of approximate solution of equation space H sphere S(x,r steepest descent transformation x₁ Xn+1