We present a new algorithm by which the Adomian polynomials can be determined for scalar-valued nonlinear polynomial functional in a Hilbert space. This algorithm calculates the Adomian polynomials without the complicated operations such as parametrization, expansion, regrouping, differentiation, etc. The algorithm involves only some matrix operations. Because of the simplicity in the mathematical operations, the new algorithm is faster and more efficient than the other algorithms previously reported in the literature. We also implement the algorithm in the MATHEMATICA code. The computing speed and efficiency of the new algorithm are compared with some other algorithms in the one-dimensional case.

翻译：我们提出一种新算法，用于在希尔伯特空间中确定标量非线性多项式泛函的阿多米安多项式。该算法无需参数化、展开、重新分组、微分等复杂操作即可计算阿多米安多项式，仅涉及若干矩阵运算。由于数学运算的简洁性，新算法比文献中先前报道的其他算法更快速、更高效。我们还以MATHEMATICA代码实现了该算法，并在单维情形下将其计算速度与效率同其他算法进行了比较。