Solving nonlinear recursions
Solving nonlinear recursions
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求解非线性递归
DOI：
10.1063/1.531702
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发表时间：
1996
影响因子：
1.3
通讯作者：
S. Havlin
中科院分区：
文献类型：
--
作者：
S. Rabinovich;G. Berkolaiko;S. Havlin
提出了一种将多项式递归映射到矩阵线性递推的一般方法。递归的解被表示为矩阵乘以初值向量的乘积。该矩阵是传递矩阵的乘积，其元素只依赖于多项式而不依赖于初始条件。该方法适用于多项式递推系统和任意阶多项式递推系统。对这些递归关系的唯一限制是，最高阶项可以作为低阶项的函数以显式形式表示(范式的存在)。文中还描述了这种方法的连续模拟。
A general method to map a polynomial recursion on a matrix linear one is suggested. The solution of the recursion is represented as a product of a matrix multiplied by the vector of initial values. This matrix is product of transfer matrices whose elements depend only on the polynomial and not on the initial conditions. The method is valid for systems of polynomial recursions and for polynomial recursions of arbitrary order. The only restriction on these recurrent relations is that the highest‐order term can be written in explicit form as a function of the lower‐order terms (existence of a normal form). A continuous analog of this method is described as well.