典型文献
Highly Accurate Latouche-Ramaswami Logarithmic Reduction Algorithm for Quasi-Birth-and-Death Process
文献摘要：
This paper is concerned with the quadratic matrix equation A0+A1X+A2X2=X where I-A0-A1-A2 is a regular M-matrix,i.e.,there exists an entrywise positive vector u such that(I-A0-A1-A2)u≥0 entry wise.It broadly includes those originally arising from the quasi-birth-and-death(QBD)process as a special case where I-A0-A1-A2 is an irreducible singular M-matrix and(A0+A1+A2)1=1 with 1 being the vector of all ones.A highly accurate implementation of Latouche-Ramaswami loga-rithmic reduction algorithm[Journal of Applied Probability,30(3):650-674,1993]is pro-posed to compute the unique minimal nonnegative solution of the matrix equation with high entry wise relative accuracy as it deserves.Numerical examples are present-ed to demonstrate the effectiveness of the proposed implementation.
文献关键词：
中图分类号：
作者姓名：
Guiding Gu;Wang Li;Ren-Cang Li
作者机构：
School of Mathematics,Shanghai University of Finance and Economics,777 Guoding Lu,Shanghai 200433,China;Department of Mathematics,University of Texas at Arlington,P.O.Box 19408,Arlington,TX 76019,USA
文献出处：
引用格式：
[1]Guiding Gu;Wang Li;Ren-Cang Li-.Highly Accurate Latouche-Ramaswami Logarithmic Reduction Algorithm for Quasi-Birth-and-Death Process)[J].数学研究（英文）,2022(02):180-194
A类：
Latouche,Ramaswami,A0+A1X+A2X2,entrywise,QBD,A0+A1+A2,loga,rithmic
B类：
Highly,Accurate,Logarithmic,Reduction,Algorithm,Quasi,Birth,Death,Process,This,paper,concerned,quadratic,matrix,equation,where,regular,there,exists,positive,vector,such,that,It,broadly,includes,those,originally,arising,from,quasi,birth,death,process,special,case,irreducible,singular,being,ones,highly,accurate,implementation,reduction,algorithm,Journal,Applied,Probability,compute,unique,minimal,nonnegative,solution,relative,accuracy,deserves,Numerical,examples,are,present,demonstrate,effectiveness,proposed
AB值：
0.523421
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