On the efficient method of solving ill-posed problems by adaptive discretization

To solve ill-posed problems Ax = f is used the Fakeev-Lardy regularization, using an adaptive discretization strategy. It is shown that for some classes of finitely smoothing operators proposed algorithm achieves the optimal order of accuracy and is more economical in the sense of amount of discrete information then standard method

Discrepancy Principle for Solving Periodic Integral Equations of the First Kind

Fully discrete projection method with discrepancy principle is considered for solving periodic integral equations of the first kind with unknown smoothness of solution. For proposed approach it is proved the optimality and effectiveness in the sense of computational resource.Розглянуто повністю дискретний проекційний метод у комбінації з принципом рівноваги для розв’язування періодичних інтегральних рівнянь у апостеріорному випадку. Доведена оптимальність та економічність такого підходу

Adaptive scheme of discretization for one semiiterative method in solving ill-posed problems

In the paper we consider a new algorithm to solving linear ill-posed problem with operators of finite smoothness. The algorithm uses one semiiterative method for the regularization of original problem in combination with an adaptive strategy of discretization. For the operators the algorithm achieves the optimal order of accuracy. Moreover, it is more economic in the sense of amount of used discrete information compare with standard methods

Combined Measurement and QCD Analysis of the Inclusive e+- p Scattering Cross Sections at HERA

A combination is presented of the inclusive deep inelastic cross sections measured by the H1 and ZEUS Collaborations in neutral and charged current unpolarised ep scattering at HERA during the period 1994-2000. The data span six orders of magnitude in negative four-momentum-transfer squared, Q^2, and in Bjorken x. The combination method used takes the correlations of systematic uncertainties into account, resulting in an improved accuracy. The combined data are the sole input in a NLO QCD analysis which determines a new set of parton distributions HERAPDF1.0 with small experimental uncertainties. This set includes an estimate of the model and parametrisation uncertainties of the fit result