Applied Mathematics & Information Sciences

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The progressive iterative approximation method (PIA) for fitting is developed in recent years. The previous research is mainly restricted to the normalized totally positive (NTP) basis. In this paper, we propose a new extended method which can unify the classic PIA method, weighted PIA method (WPIA) and local PIA (LPIA) method into one formula by introducing the transform matrix. In addition, the method presented by us has the following advantages: firstly, it can be applied to any basis; secondly, compared with other extended methods, the convergence rate of our method can be independent of the initial parameterizations; thirdly, for the NTP basis, the extended PIA method can be accelerated greatly with the fastest convergence rate. Finally, we present two numerical examples to show that our algorithm is efficient.

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