By using Frobenius matrix, this paper presents the common solution in another form to linear recurrence formula with constant coefficients.
本文利用Frobenius矩阵的自乘特性给出常系数线性递推式一般解的一种形
In this paper we consider the following class of linear recurrence with variable coefficients with two indicesu i,j =f(i,j)u i-1,j-1 +g(i,j)u i-q,j-q +h(i,j), u i,0 =c i,0 ,u 0,j =c 0,j (i,j=0,1,…),u i,j =0(i<0 or j<0),where i,j=1,2,…,q≥2,f(i,j),g(i,j) and h(i,j) (i,j≥1) are variable numbers,c i,0 and c 0,j (i,j=0,1,…) are vrbitrary constants.
本文给出了两个指标的非常系数的线性递推式的显式解 。
It is very difficult to get a clear formula solution of general linear recurrence,even for the case of homogeneous recurrence of constantcoefficients with one indicds.
根据代数方程的求解原理 ,利用传统的数学归纳方法 ,通过严密的推导得到了一类两个指标的非常系数线性递推式的显式解 ,从而为解决与之相关的定解问题 ,提供了一个统一、具体的计算公式 。