An Overview of Numerical Methods for Nonlinear Ill-Posed Problems

摘要: Publisher Summary Nonlinear ill-posed problems arise in a variety of important applications, ranging from medical imaging to geophysics the nondestructive testing materials. This chapter provides an overview various numerical methods for nonlinear problems. For each method, sequence subproblems is solved. subproblem, solution depends on parameter. The method should have following characteristics: (1) subproblem must be well-posed, (2) solved efficiently, and (3) allow inclusion priori information about desired solutions. also discusses Levenberg–Marquardt which may viewed as iterated linearize-and-then-regularize approach solving problem. As alternative Penalized Least Squares Method, it proposes constrained least squares problems, regularization comes imposing explicit bounds norm approximate solution.