We address the general mathematical problem of computing the inverse $p$-throot of a given matrix in an efficient way. A new method to construct iterationfunctions that allow calculating arbitrary $p$-th roots and their inverses ofsymmetric positive definite matrices is presented. We show that the order ofconvergence is at least quadratic and that adaptively adjusting a parameter $q$always leads to an even faster convergence. In this way, a better performancethan with previously known iteration schemes is achieved. The efficiency of theiterative functions is demonstrated for various matrices with differentdensities, condition numbers and spectral radii.
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机译：我们以有效的方式解决了计算给定矩阵的逆转$ P $ -Throot的一般数学问题。提出了一种构造允许计算任意$ P $ -th根的迭代功能的新方法及其对称正定矩阵的反转。我们展示了多级的顺序至少是二次的，并且自适应地调整参数$ Q $总是导致更快的收敛。以这种方式，实现了具有先前已知的迭代方案的更好的性能。具有不同义的矩阵的具体函数的效率，具有不同的义，条件数字和光谱半径。
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