Iterative Methods For Non-symmetric Nonlinear Problems With A Dominant Skew-Symmetric Part

In this paper, we introduce the Lanczos method for skew-symmetric indefinite system,then develop a series of Krylov method. We combine the linear methods with the nonlinearmethods, for example the Newton method, then we get the iterative methods fornon-symmetric nonlinear problems with a dominant skew-symmetric part. They have betternumerical effects than usual methods, and under reasonable assumption, to prove theirconvergence. This paper consists of four chapters.In Chapter One, we briefly introduce the background and the research significance of theskew-symmetric indefinite system and non-symmetric nonlinear problems with a dominantskew-symmetric part.In Chapter Two, we introduce the Lanczos method for skew-symmetric indefinite system,and methods of minimizing the residual, for instance, GMRESAntisym, when the system isill-conditioned, we propose the algorithms with reorthogonalization and the numericalexperiments are carried out.In Chapter Three, we derive the conjugate gradient algorithm for skew-symmetricsystem, then we get a series of methods of minimizing the error and give the correspondingnumerical experiments.In Chapter Four, we combine the linear methods with the nonlinear methods, forexample the Newton method, then we get the iterative methods for non-symmetric nonlinearproblems with a dominant skew-symmetric part. They have better numerical effects thanusual methods, and under reasonable assumption, to prove their convergence and give thecorresponding numerical experiments. At last, some conclusions are given.