Large Sparse Stable Matrix Computation

本文研究的重点是稀疏最小二乘的求解 串行和并行计算机上的问题。 利益的一个重要问题将是平等的解决 约束最小二乘问题，或者像他们经常提出的那样，等式 约束极小化问题 三种不同的方法将 检查：（1）空间方法，（2）迭代解决库恩- Tucker方程;（3）加权最小二乘法。 的方法 将从误差分析、计算 复杂性和对高性能架构的适应性。 在零空间的研究中出现了图论问题 等式约束最小二乘的一种方法， 最小二乘问题 特别是杜尔马格-门德尔松 分解的矩形矩阵将发挥作用， 所有考虑的问题的计算方面。

The focus of this research is on the solution of sparse least squares problems on sequential and parallel computers. An important problem of interest will be the solution of equality constrained least squares problems, or as they are often posed, equality constrained minimization problems. Three different approaches will be examined: (1) Null Space Methods, (2) Iterative Solution of the Kuhn- Tucker Equations, and (3) Weighted Least Squares Methods. The methods will be considered from the standpoints of error analysis, computational complexity, and adaptability to high performance architectures. Graph theoretical issues arise in the investigation of the null space approach to equality constrained least squares, and solution of sparse least squares problems. In particular, the Dulmage-Mendelsohn decomposition of a rectangular matrix will play a role in the computational aspects of all the problems considered.