A Procedure for Determining Holder Continuity

An upper bound on the Holder continuity of S is k — loga( e )/n and a lower bound k — log0( Z )/n, except that if either bound is an integer i the Holder bound is — 1,1 rather than i. 

If even tighter bounds are required, then a search further down the binary tree of submatrices can be undertaken, starting from those matrices whose norm is greater than the largest eigenvalue so far, e. A 2 -ary tree may in fact be more efficient, because each matrix with norm Z e need only be multiplied by those matrices with norm greater than e2/Z. 

Be warned that there are schemes with coefficients close to B-splines where almost all the submatrices in the tree have almost exactly the same eigenvalues. For these the above algorithm may be extremely slow. 

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