Regularization for th-order linear boundary value problems using th-order differential operators

Authors:
D. A. Kouba and John Locker

Journal:
Trans. Amer. Math. Soc. **293** (1986), 229-255

MSC:
Primary 47E05; Secondary 34B05, 47A50

DOI:
https://doi.org/10.1090/S0002-9947-1986-0814921-6

MathSciNet review:
814921

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Abstract | References | Similar Articles | Additional Information

Abstract: Let and denote real Hilbert spaces, and let be a closed densely-defined linear operator having closed range. Given an element , we determine least squares solutions of the linear equation by using the method of regularization.

Let be a third Hilbert space, and let be a linear operator with . Under suitable conditions on and and for each , we show that there exists a unique element which minimizes the functional , and the converge to a least squares solution of as .

We apply our results to the special case where is an th-order differential operator in , and we regularize using for an th-order differential operator in with . Using an approximating space of Hermite splines, we construct numerical solutions to by the method of continuous least squares and the method of discrete least squares.

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DOI:
https://doi.org/10.1090/S0002-9947-1986-0814921-6

Article copyright:
© Copyright 1986
American Mathematical Society