论文标题
部分可观测时空混沌系统的无模型预测
Parallel Computation of functions of matrices and their action on vectors
论文作者
论文摘要
我们提出了一类新的方法来计算矩阵的功能或它们在适合并行编程的向量上的作用。在并联（或计算几个矩阵的倒数）中求解适当的简单方程式系统，并通过正确的线性组合，使我们能够获得对矩阵所需功能的新高阶近似值。提出了一个错误分析以获得向前和向后错误界限。可以调整每个方法的系数，这些系数取决于处理器的数量，以提高准确性，稳定性或减少方法的圆形误差。我们通过明确构建一些方法来说明此过程，然后在几个数字示例上测试这些方法。
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of several matrices) and with a proper linear combination of the results, allows us to obtain new high order approximations to the desired functions of matrices. An error analysis to obtain forward and backward error bounds is presented. The coefficients of each method, which depends on the number of processors, can be adjusted to improve the accuracy, the stability or to reduce round off errors of the methods. We illustrate this procedure by explicitly constructing some methods which are then tested on several numerical examples.
