论文标题
Richardson和Newton-Schulz迭代的收敛率提高
Convergence Rate Improvement of Richardson and Newton-Schulz Iterations
论文作者
论文摘要
在许多关键时期和准确的关键应用程序（例如系统识别，信号和图像处理，网络处理和大数据分析，大数据分析，机器学习以及许多其他人）中，需要快速收敛，准确，可行的，可行的矩阵反转和参数估计算法。本文介绍了新的复合功率系列扩展，可选选择的速率（可以同时在具有不同计算能力的并行单元上计算出来），以进一步收敛速度提高牛顿 - 舒尔茨迭代。新的扩展已集成到Richardson迭代中，并导致了显着的收敛率提高。通过明确的瞬态模型来量化改进，以进行估计误差和模拟。此外，开发了Richardson Iteration和Newton-Schulz迭代与复合膨胀的组合的递归和计算有效版本，用于同时计算。此外，本文以功率系列扩展的工具套件的形式开发了统一的分解，这导致了一个新的计算高效牛顿 - 舒尔茨算法。
Fast convergent, accurate, computationally efficient, parallelizable, and robust matrix inversion and parameter estimation algorithms are required in many time-critical and accuracy-critical applications such as system identification, signal and image processing, network and big data analysis, machine learning and in many others. This paper introduces new composite power series expansion with optionally chosen rates (which can be calculated simultaneously on parallel units with different computational capacities) for further convergence rate improvement of high order Newton-Schulz iteration. New expansion was integrated into the Richardson iteration and resulted in significant convergence rate improvement. The improvement is quantified via explicit transient models for estimation errors and by simulations. In addition, the recursive and computationally efficient version of the combination of Richardson iteration and Newton-Schulz iteration with composite expansion is developed for simultaneous calculations. Moreover, unified factorization is developed in this paper in the form of tool-kit for power series expansion, which results in a new family of computationally efficient Newton-Schulz algorithms.
