Several Ill-posed Problem And Its Algorithm

For a given problem, if its solution is existent, unique and continually depends on thegiven input data, the problem is called well-posed, if the above problem doesn't conformto one of the three conditions, then the problem is called ill-posed. A lot of important is-sues on the application can be attributed to ill-posed problems, such as automatic control,atmospheric physics, geophysics, Cauchy problem for Laplace's equation, and so on. Theproblem has attracted the attention of scholars and researchers at home and abroad. In thisarticle, I will study solving problems for numerical diferentiation problems and the firstkind of Symm integral equation, analyse their ill-posed nature, and give the methods oftheir solution.This paper is structured as follows:The first chapter is an introduction, mainly introduces the background of ill-posedproblems, domestic and foreign research status and development trend, as well as thisarticle on research and thesis frame.The second chapter introduces the fundamental theory, involved some theoreticalknowledge in major papers: ill-posed problems, discrete ill-posed problems and regular-ization method, and provides theoretical support for follow-up study on numerical difer-entiation problems, Symm integral equations.In third chapter, we use Tikhonov regularization method, spline interpolation, trun-cated singular value decomposition method to analysis numerical diferentiation prob-lems, and give the appropriate numerical experiments.The fourth chapter mainly research the ill-posedness of Symm integral equations,and give the solving process and numerical calculation for a specific integral equations.