Polynomial Splines and Difference Equations
This is an elementary introduction to polynomial spline functions. The existence and uniqueness of the B-splines is proved. A special representation of those functions leads to many properties and, in particular, to the fact that they form a basis of the splines. The concept of linear difference equation is discussed. Eventually the connection of spline interpolation problems with linear difference equations is pointed out.
This lecture will give the simple connection between the concept of polynomial spline functions and that of linear difference equations. It therefore yields some explanation of the well-known fact that in interpolation problems with splines one has to deal with matrices of band structure.
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- G. Meinardus. Bemerkungen zur Theorie der B-Splines. Symp. Public.: Spline-Funktionen, edit. By K. Böhmer, G. Meinardus, W. Schempp. Bibl. Institut Mannheim (1974), 165–175.Google Scholar