多右端对称正定线性方程组的改进种子算法
Improved Seed Methods for Symmetric Positive Definite Linear Equations with Multiple Right-hand Sides
摘要：
本文考虑多右端对称正定线性方程组。种子共轭梯度法解决了一个右手边的共轭梯度法，同时项目的Krylov子空间，从而开发的其他右手边。然后求解下一个系统，并将其用于播种剩余的系统。共轭梯度法中的舍入误差限制了播种可以改善收敛的程度。我们提出了三个变化的种子共轭梯度法：只有第一右手边是用于播种，这个系统是解决过去的收敛，和roundantimal误差控制与一些重新正交化。我们将证明，即使在相关右侧的情况下，只有一个播种的结果实际上更好。控制舍入误差可以使第二个和随后的右侧快速收敛。
英文摘要：
We consider symmetric positive definite systems of linear equations with multiple right-hand sides. The seed conjugate gradient method solves one right-hand side with the conjugate gradient method and simultaneously projects over the Krylov subspace thus developed for the other right-hand sides. Then the next system is solved and used to seed the remaining ones. Rounding error in the conjugate gradient method limits how much the seeding can improve convergence. We propose three changes to the seed conjugate gradient method: only the first right-hand side is used for seeding, this system is solved past convergence, and the roundoff error is controlled with some reorthogonalization. We will show that results are actually better with only one seeding, even in the case of related right-hand sides. Controlling rounding error gives the potential for rapid convergence for the second and subsequent right-hand sides.
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