On differentiation of approximately given functions^†

^†Work supported by C.N.R., G.N.A.F.A.

Abstract

This paper deals with the (improperly posed) Problem of evaluating the derivative a of a function a which is approximately given. The cases when an approximation of u is given on a whole interval or on a finite sequence of fixed knots are both treated. Several a priori estimates are proved making use of an integral bound on the second derivative of u. An explicit algorithm based on the least squares methods is presented and discussed

^†Work supported by C.N.R., G.N.A.F.A.

^†Work supported by C.N.R., G.N.A.F.A.

Notes

^†Work supported by C.N.R., G.N.A.F.A.