Approximation Theorem for the First Eigenpair of Single Birth Processes  

作　　者：Yueshuang LI Lingdi WANG 

机构地区：[1]School of Statistics,Capital University of Economics and Business,Beijing 100070,P.R.China [2]School of Mathematics and Statistics,Henan University,Henan 475001,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2024年第6期825-836,共12页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant Nos.12101186,11771046);the Scientific Research Foundation for Young Teachers in Capital University of Economics and Business(Grant No.XRZ2021036)。

摘　　要：The explicit solution to the Poisson equation corresponding to the Q-matrix of a single birth process is obtained,thus the explicit inverse(if exists)is presented directly.As an application,inspired by the inverse power method,combining the explicit inverse with CollatzWielandt formula,a powerful approximation theorem for the maximal eigenpair corresponding to the Q-matrix of a single birth process is presented.Different from the classical acceleration method using some fixed shift in the iteration,the shift in each iteration step is varying and the sequence formed by these shifts is strictly monotone and increases to the eigenvalue needed,which effectively reduces the number of iterations.Some examples are studied to illustrate the power of these results.

关 键 词：single birth processes minimal eigenpair accelerated inverse power method 

分 类 号：O151.21[理学—数学]