算法937：用于奇异对称和Hermitian线性方程及最小二乘问题的MINRES-QLP
ALGORITHM 937: MINRES-QLP for Singular Symmetric and Hermitian Linear Equations and Least-Squares Problems
AI总结：
提出MINRES-QLP算法及其FORTRAN 90实现，用于求解对称或Hermitian线性系统及最小二乘问题，能处理奇异系统并计算最小长度解，克服了原MINRES算法的不稳定性。
摘要：
我们描述了算法MINRES-QLP及其FORTRAN 90实现，用于求解对称或Hermitian线性系统或最小二乘问题。如果系统是奇异的，MINRES-QLP计算唯一的最小长度解（也称为伪逆解），这通常是MINRES无法得到的。在所有情况下，它克服了原始MINRES算法中潜在的不稳定性。可以提供一个正定预条件子。我们的FORTRAN 90实现展示了一种设计模式，允许用户将问题数据提供给求解器，但使其对其他程序单元隐藏且安全。特别地，我们避免了反向通信的需求。虽然我们在此专注于FORTRAN 90实现，但我们还提供并维护MINRES和MINRES-QLP的MATLAB版本。
英文摘要：
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 preconditioner 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. While we focus here on a FORTRAN 90 implementation, we also provide and maintain MATLAB versions of MINRES and MINRES-QLP.
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