• 主题
高级搜索  >
历史搜索 清空历史
首页> 美国政府科技报告 >Algorithms for the Equilibration of Matrices and Their Application to Limited-Memory Quasi-Newton Methods
【24h】

Algorithms for the Equilibration of Matrices and Their Application to Limited-Memory Quasi-Newton Methods

机译：矩阵平衡算法及其在有限记忆拟牛顿法中的应用

获取原文
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

Diagonally scaling a matrix often reduces its condition number. Equilibration scales a matrix so that the row and column norms are equal. We review the existence and uniqueness theory for exact equilibration. Then we introduce a formalization of approximate equilibration and develop its existence and uniqueness theory. Next we develop approximate equilibration algorithms that access a matrix only by matrix-vector products. We address both the nonsymmetric and symmetric cases. Limited-memory quasi-Newton methods may be thought of as changing the metric so that the steepest-descent method works effectively on the problem. Quasi-Newton methods construct a matrix using vectors of two types involving the iterates and gradients. The vectors are related by an approximate matrix-vector product. Using our approximate matrix- free symmetric equilibration method, we develop a limited-memory quasi-Newton method in which one part of the quasi-Newton matrix approximately equilibrates the Hessian. Often a differential equation is solved by discretizing it on a sequence of increasingly fine meshes. This technique can be used when solving differential-equation-constrained optimization problems. We describe a method to interpolate our limited-memory quasi-Newton matrix from a coarse to a fine mesh.

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号