Fractal interpolation:a sequential approach

• 作者: N.Vijender M.A.Navascués
• 来源期刊: 高校应用数学学报B辑（英文版）
• 年，卷（期）: 2021,（3）
• 所属期刊栏目: Papers
• 页码范围: 330-341
• 页数: 12页
• 语种: 英文
• DOI: 10.1007/s11766-021-3635-7

摘要

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 (origi-nal) 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 α-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-α-FIFs is investigated.We identify suitable conditions on the associated scaling factors so that α-FIFs preserve r-convexity in addition to the Cr-smoothness of original function.