Error bounds for extremely ill-conditioned problems
نویسنده
چکیده
We discuss methods to compute error bounds for extremely ill-conditioned problems. As a model problem we treat matrix inversion. We demonstrate that additive corrections to improve an approximate inverse are useful for ill-conditioned problems, but hardly usable for extremely ill-conditioned problems. Here multiplicative corrections can be used, including the possibility to compute guaranteed error bounds.
منابع مشابه
Computational Experience with Rigorous Error Bounds for the Netlib Linear Programming Library
The Netlib library of linear programming problems is a well known suite containing many real world applications. Recently it was shown by Ordóñez and Freund that 71% of these problems are ill-conditioned. Hence, numerical difficulties may occur. Here, we present rigorous results for this library that are computed by a verification method using interval arithmetic. In addition to the original in...
متن کاملVerified Bounds for the p-Norm Condition Number
Methods to compute verified error bounds for the p-norm condition number of a matrix are discussed for p ∈ {1, 2,∞} and the Frobenius norm. We consider the cases of a real or complex, point or interval input matrix. In the latter case the condition number of all matrices within the interval matrix are bounded. A special method for extremely ill-conditioned matrices is derived as well. Numerical...
متن کاملA Modiication to the Gmres Method for Ill-conditioned Linear Systems
This paper concerns the use of a method for the solution of ill-conditioned linear systems. We show that the Generalized Minimum Residual Method (GMRES) in conjunction with a truncated singular value decomposition can beused to solve large nonsymmetric linear systems of equations which are nearly singular. Error bounds are given for the right s i n g u l a r v ectors and singular values compute...
متن کاملRigorous Error Bounds for the Optimal Value in Semidefinite Programming
A wide variety of problems in global optimization, combinatorial optimization as well as systems and control theory can be solved by using linear and semidefinite programming. Sometimes, due to the use of floating point arithmetic in combination with ill-conditioning and degeneracy, erroneous results may be produced. The purpose of this article is to show how rigorous error bounds for the optim...
متن کاملFloating-Point Numbers with Error Estimates (revised)
The original work [25] is here reconsidered, so many years after. The old text has been revised, plus several considerations have been added, in order to clarify some controversial aspects of the work, and to envision possible developments. A section has been added, to review the effects of the original paper. The study addresses the problem of precision in floating-point (FP) computations. A m...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006