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A Newton-type method for computing best segment approximations

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  • This paper presents a new method for computing best segment approximations. It is based on Newton iteration, but modified to obtain global convergence. The method is described in detail and a thorough convergence analysis is given. Polynomials are used as approximating functions. Not that the basic method will produce approximations that are not smooth and coninuity is not guaranteed. Howwever, we will describe applications to produce smooth spline approximation with free knots.
    Mathematics Subject Classification: 41A15, 41A50.

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