Piecewise polynomial function
= Piecewise polynomial function
A piecewise polynomial function agrees with a <polynomial> on each member of a partition. Approximation claims usually require finitely many pieces with controlled interfaces. In one dimension, finitely many partition points and localized <wavelets> with more <vanishing moments> than the polynomial degree leave only a bounded number of nonzero coefficients per scale, yielding exponential squared <best N-term approximation> error.