The concept of effective method applied to computational problems of linear algebra

摘要

A classification of computational problems is proposed which may have applications in numerical analysis. The classification utilizes the concept of effective method, which has been employed in treating decidability questions within the field of computable numbers. A problem is effectively soluble or effectively insolubles according as there is or there is not an effective method of solution. Roughly speaking, effectively insoluble computational problems are those whose general solution is restricted by an intrinsic and unavoidable computational difficulty. Some standard problems of linear algebra are analyzed to determine their type.