2 Albert Cohen , Ronald

2 Albert Cohen , Ronald A

Restricted Nonlinear Approximation 1

Albert Cohen , Wolfgang Dahmen , and Ronald Devore

We develop and analyze wavelet based adaptive schemes for nonlinear variational problems. We derive estimates for convergence rates and corresponding work counts that turn out to be asymptotically optimal. Our approach is based on a new paradigm that has been put forward recently for a class of linear problems. The original problem is transformed first into an equivalent one which is well posed...

Nonlinear Approximation and the Space

Given a function f 2 L2(Q), Q := [0, 1)2 and a real number t > 0, let U( f , t) := infg2BV (Q) kf gkL2(I) + t VQ (g), where the infimum is taken over all functions g 2 BV of bounded variation on I. This and related extremal problems arise in several areas of mathematics such as interpolation of operators and statistical estimation, as well as in digital image processing. Techniques for finding ...

Nonlinear Approximation and the Space BV(R)

Given a function f 2 L2(Q), Q := [0; 1) and a real number t > 0, let U(f; t) := infg2BV(Q) kf gk 2 L2(I) + tVQ(g); where the in mum is taken over all functions g 2 BV of bounded variation on I. This and related extremal problems arise in several areas of mathematics such as interpolation of operators and statistical estimation, as well as in digital image processing. Techniques for nding minimi...