Ill-Posed Problems with A Priori Information

摘要: Part 1 Unstable problems: base formulations of problems ill-posed examples and its stability analysis the classification methods for unstable with a priori information. 2 Iterative approximation fixed points their application to basic classes mappings convergence theorems iterative processes iterations correcting multipliers applications mathematical programming regularizing properties averaging regularization variation inequalities operator equations monotone operators in partially-ordered spaces schemes based on Gauss-Newton method. 3 Regularization symmetric spectral L-basis linear kernel analogies Tikhonov's Lavent'ev's variational residual method quasisolutions generalized problem. 4 The finite-moment problem systems equations: statement finite-dimensional approximations basis projections Fejer FMP Hilbert reproducing kernels solution equation system. 5 Discrete algorithms: discrete elements algorithm integral interpolation approximate solutions by splines reconstuction regularized algorithms discontinuous functions classes. 6 Numerical applications: solving gravimetry computing experiment data processing structure investigations amorphous alloys. Appendix: correction parameters first kind.