Abstract
In this chapter we will consider the approximate solution of integral equations of the second kind by replacing the kernels by degenerate kernels,i.e., by approximating a given kernel K(x,y)through a sum of a finite number of products of functions of xalone by functions of yalone. In particular, we will describe the construction of appropriate degenerate kernels by interpolation of the given kernel and by orthonormal expansions. The corresponding error analysis will be settled by our results in Section 10.1. We also include a discussion of some basic facts on piecewise linear interpolation and trigonometric interpolation, which will be used in this and subsequent chapters.
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© 1999 Springer Science+Business Media New York
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Kress, R. (1999). Degenerate Kernel Approximation. In: Linear Integral Equations. Applied Mathematical Sciences, vol 82. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0559-3_11
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DOI: https://doi.org/10.1007/978-1-4612-0559-3_11
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6817-8
Online ISBN: 978-1-4612-0559-3
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