one of the main steps within the geoid computation methodology without applying the stokes formula is downward continuation of the harmonic residual observables from the surface of the earth down to the surface of the reference ellipsoid. this downward continuation is done via the abel-poisson integral and its derivatives. this integral in which the unknowns, i.e. harmonic residual potential va...

A simple proof of the convergence of the variational regularization, with the regularization parameter, chosen by the discrepancy principle, is given for linear operators under suitable assumptions. It is shown that the discrepancy principle, in general, does not yield uniform with respect to the data convergence. An a priori choice of the regularization parameter is proposed and justified for ...

The aim of this note is to prove a new discrepancy principle. The advantage of the new discrepancy principle compared with the known one consists of solving a minimization problem (see problem (2) below) approximately, rather than exactly, and in the proof of a stability result. To explain this in more detail, let us recall the usual discrepancy principle, which can be stated as follows. Consid...

Let Ay = f , A is a linear operator in a Hilbert space H, y ⊥ N (A) := {u : Au = 0}, R(A) := {h : h = Au, u ∈ D(A)} is not closed, f δ − f ≤ δ. Given f δ , one wants to construct u δ such that lim δ→0 u δ − y = 0. A version of the DSM (dynamical systems method) for finding u δ consists of solving the problem ˙ u δ (t) = −u δ (t) + T −1 a(t) A * f δ , u(0) = u 0 , (*) where T := A * A, T a := T ...

Abstract. The χ-principle generalizes the Morozov discrepancy principle to the augmented residual of the Tikhonov regularized least squares problem. For weighting of the data fidelity by a known Gaussian noise distribution on the measured data and, when the stabilizing, or regularization, term is considered to be weighted by unknown inverse covariance information on the model parameters, the mi...

This paper reports on an optimum dynamic programming (DP) based time-normalization algorithm for spoken word recognition. First, a general principle of time-normalization i s given using timewarping function. Then, two time-normalized distance definitions, d e d symmetric and asymmetric forms, are derived from the principle. These two forms are compared with each other through theoretical discu...