首页|Approximation Theorem for the First Eigenpair of Single Birth Processes
Approximation Theorem for the First Eigenpair of Single Birth Processes
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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 Collatz-Wielandt 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.
single birth processesminimal eigenpairaccelerated inverse power method
Yueshuang LI、Lingdi WANG
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School of Statistics,Capital University of Economics and Business,Beijing 100070,P.R.China
School of Mathematics and Statistics,Henan University,Henan 475001,P.R.China
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