About global and local orthogonal splines

Title	About global and local orthogonal splines
Authors	V. L. Leontiev¹ ¹Peter the Great St. Petersburg Polytechnic University
Annotation	The procedures of orthogonalization of splines generating global or local orthogonal splines are considered. It is noted that many existing orthogonalization procedures for the formation of local orthogonal splines make it possible to minimize sizes growth of splines compact supports, but initial sizes of compact supports increases during orthogonalization. The importance of Leontiev theory of splines, based on obtaining local orthogonal splines using the orthogonalization procedure that preserves sizes of compact supports of splines, is emphasized.
Keywords	basis of Hilbert space, Haar functions, Faber functions, Franklin functions, Schoenberg splines, global or local orthogonal splines, orthogonalization procedure preserving compact supports of functions, Gram-Schmidt orthogonalization procedure.
Citation	Leontiev V. L. ''About global and local orthogonal splines'' [Electronic resource]. Mathematical modeling, numerical methods, and software systems: Collection of materials from the 12th All‑Russian Scientific Youth School‑Seminar named after E. V. Voskresensky (Saransk, July 21–24, 2026). - pp. 258-260. Available at: https://conf.svmo.ru/files/2026/papers/paper118.pdf. - Date of access: 25.09.2026.