Fractal interpolation is a modern technique to fit and analyze scientific data.We develop a new class of fractal interpolation functions which converge to a data generating(original)function for any choice of the scal...Fractal interpolation is a modern technique to fit and analyze scientific data.We develop a new class of fractal interpolation functions which converge to a data generating(original)function for any choice of the scaling factors.Consequently,our method offers an alternative to the existing fractal interpolation functions(FIFs).We construct a sequence of-FIFs using a suitable sequence of iterated function systems(IFSs).Without imposing any condition on the scaling vector,we establish constrained interpolation by using fractal functions.In particular,the constrained interpolation discussed herein includes a method to obtain fractal functions that preserve positivity inherent in the given data.The existence of Cr--FIFs is investigated.We identify suitable conditions on the associated scaling factors so that-FIFs preserve r-convexity in addition to the Cr-smoothness of original function.展开更多
基金Supported by Council of Scienti c&Industrial Research(CSIR),India(25(0290)/18/EMR-II).
文摘Fractal interpolation is a modern technique to fit and analyze scientific data.We develop a new class of fractal interpolation functions which converge to a data generating(original)function for any choice of the scaling factors.Consequently,our method offers an alternative to the existing fractal interpolation functions(FIFs).We construct a sequence of-FIFs using a suitable sequence of iterated function systems(IFSs).Without imposing any condition on the scaling vector,we establish constrained interpolation by using fractal functions.In particular,the constrained interpolation discussed herein includes a method to obtain fractal functions that preserve positivity inherent in the given data.The existence of Cr--FIFs is investigated.We identify suitable conditions on the associated scaling factors so that-FIFs preserve r-convexity in addition to the Cr-smoothness of original function.
