Nonlinear Ill-posed Problems

Often many scientific, technological and engineering problems turn out to be ill-pose; meaning they have no solution, no unique solution or an unstable solution. Where searching generalized solutions fails to solve the problem, regularizing algorithms of discrepancy, quasisolutions and smoothing functions are used. Professor A N Tikhonov was the founder of non-linear ill-posed problem theory. This two-volume book introduces the reader to the theory, and shows its applications in the natural sciences. The first volume introduces the foundations of the theory, and provides the necessary background for the design of new numerical methods. The second volume presents the finite-dimensional variants and modifications of these methods to help readers use current computer software. It considers applications in linear algebra, vibrational spectroscopy, astrophysics and medicine. This book should be of interest to researchers and specialists in numerical mathematics, geophysics and astrophysics, optics and spectroscopy, plasma physics, heat conduction and acoustics.