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带约束最小二乘问题的数值求解方法

Numerical Methods for Solving Least Squares Problems with Constraints
课程网址: http://videolectures.net/mlws04_gene_nmsls/  
主讲教师: Gene Golub
开课单位: 斯坦福大学
开课时间: 2007-02-25
课程语种: 英语
中文简介:
在本次演讲中,我们讨论了利用线性约束和/或二次约束求解线性最小二乘问题和最小二乘问题的问题。当数据矩阵是单数或近似单数时,我们特别感兴趣开发稳定的数值方法。特别感兴趣的是大且稀疏的矩阵,并且必须采用迭代方法。二次约束问题出现在需要正则化的问题中。对于这些问题,需要拉格朗日乘数,并且计算可能非常密集。我们提出的方法将快速产生参数的估计并允许找到最小二乘解。
课程简介: In this talk, we discuss the problem of solving linear least squares problems and Total Least Squares problems with linear constraints and/or a quadratic constraint. We are particularly interested in developing stable numerical methods when the data matrix is singular or near singular. Of particular interest are matrices which are large and sparse and for which iterative methods must be employed. The quadratically constrained problems arise in problems where regularization is required. For such problems, a Lagrange multiplier is required and that calculation may be quite intensive. The method we propose will quickly yield an estimate of the parameter and allow for finding the least squares solution.
关 键 词: 线性约束; 最小二乘问题; 数据矩阵
课程来源: 视频讲座网
最后编审: 2019-07-24:cwx
阅读次数: 83