On the approximation to solutions of operator equations by the least squares method.

Autor: M. L. Gorbachuk
Zdroj: Functional Analysis & Its Applications; Jan2005, Vol. 39 Issue 1, p71-75, 5p
Abstrakt: Abstract We consider the equation Au = f, where A is a linear operator with compact inverse A-1 in a separable Hilbert space H. For the approximate solution un of this equation by the least squares method in a coordinate system {ek}k?N that is an orthonormal basis of eigenvectors of a self-adjoint operator B similar to A ( $$\mathcal{D}$$ (B) = $$\mathcal{D}$$ (A)), we give a priori estimates for the asymptotic behavior of the expressions rn = ?un - u? and Rn = ?Aun - f? as n ? 8. A relationship between the order of smallness of these expressions and the degree of smoothness of u with respect to the operator B is established. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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