Safe Starting Regions for Iterative Methods

Global Two-Scalar Velocimetry and Development of Low-Order Models for Use in Optical-Phase Correction in a Plane Mixing Layer

“…These methods find all solutions of (1) in a finite domain. As discussed by Moore and Jones ( [9], p. 1056), three possibilities arise when examining such a finite domain. One is sometimes able to show that no solution exists, or that at least one solution exists.…”

Solution of finite systems of equations by interval iteration

“…In this case, however, the interval iteration process (4.1) is 6inite, and will tde'nunate in either the condition ztaled. The difficulty concerning existence can be resolved by applying some other existence test than (4.4) to X = XN, a region which will be smaller than X 0 unless the iteration stalled, or x can be divided into subregions for further investigation, using the algorithm of Moore and Jones, which has also been shown to be finite if G is sufficiently fine [13], [14].…”

A Theory of Interval Iteration

“…(Y°m ay be the limit Y* if obtained in a finite number of steps, or otherwise.) Possible alternatives in this situation include partition of the resulting interval Y°i nto subintervals for further examination, a strategy developed by Moore and Jones [9], or acceptance of Y° as a generalized or pseudosolution (relative to the initial interval Y0) of the fixed point problem. This latter choice may be useful in the development of an interval version of regularization of solutions of ill-posed problems.…”