In our work, we consider the linear least squares problem for m × n-systems of linear equations Ax = b, m ≥ n, such that the matrix A and right-hand side vector b can vary within an interval m × n-matrix A and an interval m-vector b, respectively. We have to compute, with a prescribed accuracy, outer coordinate-wise estimates of the set of all least squares solutions to Ax = b for A ∈A and b ∈b. 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 interval least squares problem under solution. 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.

在我们的工作中，我们考虑线性最小二乘问题为米× Ñ线性方程-systems甲X = b，米≥ Ñ，使得基质甲和右手侧矢量b可以在间隔内变化米× ñ -矩阵A和间隔m-向量b。我们必须计算，以规定的精度，该组所有的最小二乘解的的外坐标明智估计甲X = b为甲∈甲和b ∈ b。本文致力于解决所谓的PPS方法（基于参数集的划分）以解决上述问题。我们将与线性最小二乘问题相关联的正态方程组简化为特殊的扩展矩阵形式，并生成一个线性方程组的对称区间系统，该系统等效于求解中的区间最小二乘问题。为了解决这种对称系统，我们提出了一种称为ILSQ-PPS的PPS方法的新结构，该方法可以以实际效率估算解决方案集的封闭性。为了演示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。