论文标题
pps方法解决间隔线性最小二乘问题
Solving interval linear least squares problems by PPS-methods
论文作者
论文摘要
在我们的工作中，我们考虑了线性最小二乘问题的线性最小二乘问题$ \ times n $ - 系统线性方程式$ ax = b $，$ m \ geq n $，因此矩阵$ a $ a $ a $ a $ a $ a $ a $ b $ b $在间隔$ m \ times $ m \ times n $ -mmatrix和Interval $ m $ m $ $ m $ -m-vector中可以变化。当$ a $ a $和$ b $在其间隔范围内独立变化时，我们必须尽可能清晰地计算出最小二乘解决方案的间隔围墙。我们的文章致力于开发所谓的PPS方法（基于参数集的分区）来解决上述问题。我们将与线性的平方问题相关的正常方程式系统减少到特殊的扩展矩阵形式，并产生与原始间隔最小二乘问题相同的线性方程式的对称间隔系统。为了解决此类对称系统，我们提出了一种称为ILSQ-PPS的PPS方法的新结构，该构建以实用效率估算溶液集合的外壳。为了证明ILSQ-PPS方法的功能，我们提出了许多数值测试，并将其结果与其他方法获得的结果进行比较。
In our work, we consider the linear least squares problem for $m\times n$-systems of linear equations $Ax = b$, $m\geq n$, such that the matrix $A$ and right-hand side vector $b$ can vary within an interval $m\times n$-matrix and an interval $m$-vector respectively. We have to compute, as sharp as possible, an interval enclosure of the set of all least squares solutions to $Ax = b$ when $A$ and $b$ independently vary within their interval bounds. Our article is devoted to the development of the so-called PPS-methods (based on Partitioning of the Parameter Set) to solve the above problem. We reduce the normal equation system, associated with the linear lest squares problem, to a special extended matrix form and produce a symmetric interval system of linear equations that is equivalent to the original interval least squares problem. To solve such symmetric system, we propose a new construction of PPS-methods, called ILSQ-PPS, which estimates the enclosure of the solution set with practical efficiency. To demonstrate the capabilities of the ILSQ-PPS method, we present a number of numerical tests and compare their results with those obtained by other methods.
