Total Least Norm Formulation and Solution for Structured Problems
Total Least Norm Formulation and Solution for Structured Problems
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DOI：
10.1137/s0895479893258802
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
J. B. Rosen;Haesun Park;J. Glick
中科院分区：
文献类型：
--
作者：
J. B. Rosen;Haesun Park;J. Glick
一个新的配方和算法计算的解决方案，超定线性系统，$Ax \approx B$，在$A$和$B$可能的错误。这种方法保留了$A$或$[A \：|\：B]$，如Toeplitz或稀疏结构，并最小化离散$L_p$范数中的误差测量，其中$p= 1，2 $或$\infty$。它可以被认为是总体最小二乘的推广，我们称之为结构总体最小范数（STLN）。STLN问题制定，其解决方案的算法，并分析，计算结果，说明算法的收敛性和性能的各种结构化的问题进行了总结。对于每个测试问题，最小二乘，总最小二乘，STLN与$p = 1，2，$和$\infty$得到的解决方案进行了比较。这些结果证实了STLN算法是解决$A$或$B$具有特殊结构或错误仅发生在$A$和$B$的某些元素中的问题的有效方法。
A new formulation and algorithm is described for computing the solution to an overdetermined linear system, $Ax \approx b$, with possible errors in both $A$ and $b$. This approach preserves any affine structure of $A$ or $[A \:|\:b]$, such as Toeplitz or sparse structure, and minimizes a measure of error in the discrete $L_p$ norm, where $p=1,2$, or $\infty$. It can be considered as a generalization of total least squares and we call it structured total least norm (STLN). The STLN problem is formulated, the algorithm for its solution is presented and analyzed, and computational results that illustrate the algorithm convergence and performance on a variety of structured problems are summarized. For each test problem, the solutions obtained by least squares, total least squares, and STLN with $p = 1,2,$ and $\infty$ were compared. These results confirm that the STLN algorithm is an effective method for solving problems where $A$ or $b$ has a special structure or where errors can occur in only some of the elements of $A$ and $b$.