线性回归模型的QR参数估计

应用矩阵的 QR分解 ,对线性回归模型 Y=Yβ+ U进行参数估计 ,如 QR成功分解 ,此法比普通最小—乘法 ( OLS)简捷 .     

Two-stage least squares and indirect least squares algorithms for simultaneous equations models

This paper analyzes the solution of simultaneous equations models. Efficient algorithms for the two-stage least squares method using QR-decomposition are developed and studied. The reduction of the execution time when the structure of the matrices in each equation is exploited is analyzed theoretically and experimentally. An efficient algorithm for the indirect least squares method is developed. Some techniques are used to accelerate the solution of the problem: parallel versions for multicore systems, and extensive use of the MKL library, thus obtaining efficient, portable versions of the algorithms.     

Using qr-decompositions in the numerical solution of linear recurrence relations

For the numerically stable calculation of a solution of a linear recurrence relation the degree of minimality of this solution has to be known. One method to determine the degree of minimality is by calculating the asymptotic behavior of all solutions, a task which is difficult to accomplish for many types of recurrence relations. In this paper we describe a method which uses QR-decomposition for the determination of the degree of minimality