摘要 : After a brief survey of basic results about finite-dimensional approximation settings(such as mathematical frameworks of various projection methods, including the least-squares method,the dual least-squares method, and the Galerki... 展开 After a brief survey of basic results about finite-dimensional approximation settings(such as mathematical frameworks of various projection methods, including the least-squares method,the dual least-squares method, and the Galerkin method) for infinite-dimensional Moore-Penroseinverses, this paper proceeds to a detailed study from the following aspects: For projection methods,we investigate convergence and weak convergence of their approximation setting to develop a unifiedtheory on projection methods for infinite-dimensional Moore-Penrose inverses; this investigationyields a fundamental convergence theorem (Theorem 2.2), from which the criterion for convergence,the criterion for weak convergence, and the generalized dual least-squares method are derived. Wealso derive general results on the least-squares method, by which two flaws in Groestch's results arecorrected. For nonprojection methods (whose approximation setting is a more general framework),we investigate weak perfect convergence of their approximation setting and provide a necessaryand sufficient condition of such convergence holding (Theorem 3.2). Several examples are proposedas counterexamples to illustrate the differences between some important concepts or as concretealgorithms to show how the present work can help to analyze their behavior. 收起