Choi Sou-Cheng T, Saunders Michael A
University of Chicago/Argonne National Laboratory.
Stanford University.
ACM Trans Math Softw. 2014 Feb;40(2). doi: 10.1145/2527267.
We describe algorithm MINRES-QLP and its FORTRAN 90 implementation for solving symmetric or Hermitian linear systems or least-squares problems. If the system is singular, MINRES-QLP computes the unique minimum-length solution (also known as the pseudoinverse solution), which generally eludes MINRES. In all cases, it overcomes a potential instability in the original MINRES algorithm. A positive-definite pre-conditioner may be supplied. Our FORTRAN 90 implementation illustrates a design pattern that allows users to make problem data known to the solver but hidden and secure from other program units. In particular, we circumvent the need for reverse communication. Example test programs input and solve real or complex problems specified in Matrix Market format. While we focus here on a FORTRAN 90 implementation, we also provide and maintain MATLAB versions of MINRES and MINRES-QLP.
我们描述了用于求解对称或埃尔米特线性系统或最小二乘问题的算法MINRES - QLP及其FORTRAN 90实现。如果系统是奇异的，MINRES - QLP会计算唯一的最小长度解（也称为伪逆解），而MINRES通常无法得到该解。在所有情况下，它都克服了原始MINRES算法中可能存在的不稳定性。可以提供一个正定预处理器。我们的FORTRAN 90实现展示了一种设计模式，该模式允许用户使求解器知道问题数据，但对其他程序单元隐藏且安全。特别是，我们避免了反向通信的需求。示例测试程序输入并求解以矩阵市场格式指定的实问题或复问题。虽然我们在此重点关注FORTRAN 90实现，但我们也提供并维护MINRES和MINRES - QLP的MATLAB版本。
