MATHEMATICAL PROGRAMMING AND THE NUMERICAL SOLUTION OF LINEAR EQUATIONS.
MATHEMATICAL PROGRAMMING AND THE NUMERICAL SOLUTION OF LINEAR EQUATIONS.
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数学规划和线性方程的数值解。
DOI：
10.2307/2285796
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发表时间：
1976
影响因子：
3.7
通讯作者：
W. R. Burrus
中科院分区：
文献类型：
--
作者：
B. Rust;W. R. Burrus
摘要：这本书关注的是使用数学规划技术解决病态系统的线性方程组与各种错误的右手边向量。这项工作的主要动机是实验物理的频谱展开问题，因此处理也包括第一类Fredholm积分方程，它可以被认为是一个无限维病态系统。开发的新技术的基本思想是使用先验知识的解决方案，以大大减少的解决方案是一致的右手边的错误的类的大小。该方法的目的是给区间估计的解决方案-的大小的区间被确定的大小的错误在右手边，和约束施加在类的可接受的解决方案的先验信息。所使用的基本先验约束是，解决方案必须是非负的，但它表明，许多其他先验约束可以减少到一个简单的非负性约束的一个适当的变量变换。当考虑到非负约束时，估计解的上下界的问题可以用数学规划问题来表示和求解。这本书对待的情况下，右手边的错误是绝对已知的谎言在一些有界区域，也是情况下，错误是正态分布。（作者）
Abstract : The book is concerned with the use of mathematical programming techniques for solving ill-conditioned systems of linear equations with various kinds of errors in the right hand side vector. The primary motivation for the work was the spectrum unfolding problem of experimental physics, so the treatment also includes the Fredholm integral equation of the first kind, which can be considered to be an infinite dimensional ill-conditioned system. The basic idea of the new techniques which are developed is the use of priori knowledge about the solution in order to greatly reduce the size of the class of solutions which are consistent with the right hand side errors. The methods are designed to give interval estimates for the solution--the sizes of the intervals being determined by the sizes of the errors in the right hand side, and the constraints imposed on the class of acceptable solutions by the a priori information. The basic a priori constraint which is used is that the solution must be non-negative; but it is shown that many other a priori constraints can be reduced to a simple non-negativity constraint by a suitable transformation of variables. When the non-negativity constraint is taken into account, the problem of estimating lower and upper bounds for the solution can be formulated and solved as a mathematical programming problem. The book treats both the case where the right hand side errors are known absolutely to lie in some bounded region and also the case where the errors are normally distributed. (Author)