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A new efficient orthogonalization of the B-spline basis is proposed andcontrasted with some previous orthogonalized methods. The resulting orthogonalbasis of splines is best visualized as a net of functions rather than asequence of them. For this reason, the basis is referred to as a splinet. Thesplinets feature clear advantages over other spline bases. They efficientlyexploit 'near-orthogonalization' featured by the B-splines and gains areachieved at two levels: locality that is exhibited through small size of thetotal support of a splinet and computational efficiency that follows from asmall number of orthogonalization procedures needed to be performed on theB-splines to achieve orthogonality. These efficiencies are formally proven byshowing the asymptotic rates with respect to the number of elements in asplinet. The natural symmetry of the B-splines in the case of the equallyspaced knots is preserved in the splinets, while quasi-symmetrical features arealso seen for the case of arbitrarily spaced knots.

Splinets -- efficient orthonormalization of the B-splines