正交累积投影法用于线性方程组
Orthogonally Accumulated Projection Methods for Linear System of Equations
AI总结：
本文提出了一种求解线性方程组的正交累积投影方法，通过高效构造正交向量序列，利用内积快速获取解，实现有限次迭代求解。
摘要：
本文提出了一种迭代正交累积投影方法，用于求解线性方程组。该方法是最近作者提出累积投影（AP）技术的应用。与原始AP方法不同，这些方法尝试高效构造正交向量序列，使得解与序列中每个向量的内积可快速计算，从而在精确运算下有限次迭代内获取解。我们还讨论了处理构造正交向量过程中失去正交性的策略。提供了数值实验以展示这些方法的效率。
英文摘要：
A type of iterative orthogonally accumulated projection methods for solving linear system of equations are proposed in this paper. This type of methods are applications of accumulated projection(AP) technique proposed recently by authors. Instead of searching projections in a sequence of subspaces as done in the original AP approach, these methods try to efficiently construct a sequence of orthonormal vectors while the inner-product between the solution to the system and each vector in the sequence can be easily calculated, thus the solution can be retrieved in finite number of iterations in case of exact arithmetic operations. We also discuss the strategies to handle loss-of-orthogonality during the process of constructing orthonormal vectors. Numerical experiments are provided to demonstrate the efficiency of these methods.
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