Constrained Approximation Techniques for Solving Integral Equations
The two standard techniques for numerically solving integral equations are collocation and Galerkin. Both these methods find an approximation via interpolation in that an approximating subspace of dimension n is provided, and the n parameters are found by solving n equations. These methods work well in practice for many equations as is seen for example in [1,2]. However, circumstances may arise when due to numerical error the number of basis functions n needs to be increased to an excessively large value. Also many real problems prescribe conditions on the underlying function, thus constraints on the approximation are introduced. Both these problems can be overcome if instead of interpolating we consider the approximation problem.
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