# Smoothest interpolation with boundary conditions in $W^3_2[a,b]$

 Title Smoothest interpolation with boundary conditions in $W^3_2[a,b]$ Publication Type Journal Article Year of Publication 2019 Authors Ivanova V, Uluchev R Journal Annuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique Volume 106 Start Page 153 Pagination 153-174 ISSN 1313-9215 (Print) 2603-5529 (Online) Keywords Birkhoff interpolation, Smoothest interpolation, splines Abstract We study the problem on the smoothest interpolant with boundary conditions in the Sobolev space $W^3_2[a,b]$. Characterization and uniqueness of the best interpolant with free knots of interpolation, satisfying boundary conditions, are proved. Based on our proofs we present an algorithm for finding the unique oscillating spline interpolant. Numerical results are given. 2010 MSC 65D05, 65D07
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