A new algorithm for 5-band Toeplitz matrix inversion with application to GCV smoothing spline computation (Q1808686)
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scientific article; zbMATH DE number 1369614
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A new algorithm for 5-band Toeplitz matrix inversion with application to GCV smoothing spline computation |
scientific article; zbMATH DE number 1369614 |
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A new algorithm for 5-band Toeplitz matrix inversion with application to GCV smoothing spline computation (English)
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9 February 2000
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A new algorithm for computing the inverse of a 5-band Toeplitz matrix in \(O(n^2)\) operations is developed. A nice feature of this algorithm is that it can compute individual entries of the inverse efficiently (in constant time). As an application of this algorithm, the author presents a way to compute the generalized cross validation (GCV) smoothing spline in linear time for equally spaced data case. The GCV method was proposed by \textit{P. Craven} and \textit{G. Wahba} [Numer. Math. 31, 377-403 (1979; Zbl 0413.65080)].
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Toeplitz matrix
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inverse matrix
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smoothing splines
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generalized cross validation
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divided differences
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algorithm
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