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改进的cgls迭代正则化法在内插平面坐标转换中的应用

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测绘与空间地理信息 2019年第2期42卷 44-45,49页

作者：倪飞申佳南通航运职业技术学院船舶与海洋工程系江苏南通226010

内插算法用于测量平面坐标转换时,经常会遇到因矩阵的病态导致坐标转换精度差、甚至转换失败的问题。文章基于改进的cgls迭代正则化算法进行抗病态研究。算例研究表明,改进后的算法能够很好地消除病态矩阵影响,获得相对较高精度的转换... 详细信息

内插算法用于测量平面坐标转换时,经常会遇到因矩阵的病态导致坐标转换精度差、甚至转换失败的问题。文章基于改进的cgls迭代正则化算法进行抗病态研究。算例研究表明,改进后的算法能够很好地消除病态矩阵影响,获得相对较高精度的转换坐标。

关键词：内插最小二乘法 cgls

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基于cgls求解坐标转换参数

矿山测量 2010年第5期38卷 55-57页

作者：李云云冯遵德徐州师范大学测绘学院江苏徐州221116

坐标转换是一项重要的计算工作,而转换参数的求解是坐标转换计算工作的关键问题之一。在转换参数的求解中如何克服或减弱病态问题对转换参数求解的影响,是提高转换参数精度的重要措施。文中运用几种典型的处理病态问题的方法求解转换参... 详细信息

坐标转换是一项重要的计算工作,而转换参数的求解是坐标转换计算工作的关键问题之一。在转换参数的求解中如何克服或减弱病态问题对转换参数求解的影响,是提高转换参数精度的重要措施。文中运用几种典型的处理病态问题的方法求解转换参数,通过分析比较认为cgls法效果较优。针对cgls法提出了基于坐标差平方和最小作为迭代结束的条件,在实施过程中证明是合理可行的。

关键词：坐标转换参数病态问题 cgls

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基于cgls求解坐标转换参数

基于CGLS求解坐标转换参数

SOME PROPERTIES OF LSQR FOR LARGE SPARSE LINEAR LEAST SQUARES PROBLEMS

第二届“测绘科学前沿技术论坛”

作者：冯遵德李云云徐州师范大学测绘学院

坐标转换计算是一项重要的工作,而转换参数的求解是坐标转换计算工作的关键问题之一。转换参数精度的高低决定着坐标转换的精度高低。在转换参数的求解中往往存在病态问题,因此克服或减弱病态问题对转换参数求解的影响,是数据处理的目... 详细信息

坐标转换计算是一项重要的工作,而转换参数的求解是坐标转换计算工作的关键问题之一。转换参数精度的高低决定着坐标转换的精度高低。在转换参数的求解中往往存在病态问题,因此克服或减弱病态问题对转换参数求解的影响,是数据处理的目标。本文运用几种典型的处理病态问题的方法求解转换参数,分析比较,认为cgls法效果较优。针对cgls法提出基于坐标差平方和最小作为迭代结束的条件,在实施过程中证明是合理可行的。

关键词：坐标转换参数病态问题 cgls

来源： cnki会议评论

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Journal of Systems Science & Complexity 2010年第4期23卷 815-821页

作者： Zhongxiao JIA Department of Mathematical Sciences,Tsinghua University,Beijing 100084,China. Department of Mathematical Sciences Tsinghua University

It is well-known that many Krylov solvers for linear systems,eigenvalue problems,andsingular value decomposition problems have very simple and elegant formulas for residual *** not only allow us to further understand the methods theoretically but also can be usedas cheap stopping criteria without forming approximate solutions and residuals at each step beforeconvergence takes *** for large sparse linear least squares problems is based on the Lanczosbidiagonalization process and is a Krylov ***,there has not yet been an analogouslyelegant formula for residual *** paper derives such kind of *** addition,the authorgets some other properties of LSQR and its mathematically equivalent cgls.

关键词： cgls krylov subspace lanczos bidiagonalization least squares lsqr normal equations.

Some results on the regularization of LSQR for large-scale discrete ill-posed problems

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Science China Mathematics 2017年第4期60卷 701-718页

作者： HUANG Yi JIA ZhongXiao Department of Mathematical Sciences Tsinghua University Beijing 100084 China

LSQR, a Lanczos bidiagonalization based Krylov subspace iterative method, and its mathematically equivalent conjugate gradient for least squares problems(cgls) applied to normal equations system, are commonly used for large-scale discrete ill-posed problems. It is well known that LSQR and cgls have regularizing effects, where the number of iterations plays the role of the regularization parameter. However, it has long been unknown whether the regularizing effects are good enough to find best possible regularized solutions. Here a best possible regularized solution means that it is at least as accurate as the best regularized solution obtained by the truncated singular value decomposition(TSVD) method. We establish bounds for the distance between the k-dimensional Krylov subspace and the k-dimensional dominant right singular space. They show that the Krylov subspace captures the dominant right singular space better for severely and moderately ill-posed problems than for mildly ill-posed problems. Our general conclusions are that LSQR has better regularizing effects for the first two kinds of problems than for the third kind, and a hybrid LSQR with additional regularization is generally needed for mildly ill-posed problems. Exploiting the established bounds, we derive an estimate for the accuracy of the rank k approximation generated by Lanczos bidiagonalization. Numerical experiments illustrate that the regularizing effects of LSQR are good enough to compute best possible regularized solutions for severely and moderately ill-posed problems, stronger than our theory, but they are not for mildly ill-posed problems and additional regularization is needed.

关键词： ill-posed problem regularization Lanczos bidiagonalization LSQR cgls hybrid