Data fitting by spline functions using the biorthonormal basis of the B-spline basis

The basis for the spline function space which is orthogonal to the B-spline basis is derived, i.e. the biorthonormal basis of the B-spline basis. The derived basis makes it easy to obtain B-spline coefficients from a given function in a straightforward way. This is applied to data fitting by spline functions, which uses the least square approximation. Then computing quantities and errors are examined, and the effectiveness and potential of this approach is described.