Motivated by the effort to understand the mathematical structure underlying the Teukolsky equations in a Kerr metric background, a homogeneous integral equation related to the prolate spheroidal function is studied. F...Motivated by the effort to understand the mathematical structure underlying the Teukolsky equations in a Kerr metric background, a homogeneous integral equation related to the prolate spheroidal function is studied. From the consideration of the Fredholm determinant of the integral equation, a family of generalized error function is defined, with which the Fredholm determinant of the sinc kernel is also evaluated. An analytic solution of a special ease of the fifth Painlev~ transcendent is then worked out explicitly.展开更多
In this paper we propose an efficient and robust method for computing the analytic center of the polyhedral set P={x€R^n|Ax=b,x>0},where the matrix A€ Rm×n is ill-conditioned,and there are errors in A and b.Be...In this paper we propose an efficient and robust method for computing the analytic center of the polyhedral set P={x€R^n|Ax=b,x>0},where the matrix A€ Rm×n is ill-conditioned,and there are errors in A and b.Besides overcoming the difficulties caused by ill-cond计ioning of the matrix A and errors in A and b,our method can also detect the infeasibility and the unboundedness of the polyhedral set P automatically during the compu tation.Det ailed mat hematical analyses for our method are presen ted and the worst case complexity of the algorithm is also given.Finally some numerical results are presented to show the robustness and effectiveness of the new method.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 11171329,11203003 and 11373013
文摘Motivated by the effort to understand the mathematical structure underlying the Teukolsky equations in a Kerr metric background, a homogeneous integral equation related to the prolate spheroidal function is studied. From the consideration of the Fredholm determinant of the integral equation, a family of generalized error function is defined, with which the Fredholm determinant of the sinc kernel is also evaluated. An analytic solution of a special ease of the fifth Painlev~ transcendent is then worked out explicitly.
基金The authors would like to thank two anonymous referees for their valuable comments and suggestions.The author Yu-hong Dai is supported by the Chinese Natural Science Foundation(Nos.11631013,71331001 and 11331012)the National 973 Program of China(No.2015CB856002)The author Fengmin Xu is supported by the Chinese NSF grants(Nos.11571271,11631013 and 11605139).
文摘In this paper we propose an efficient and robust method for computing the analytic center of the polyhedral set P={x€R^n|Ax=b,x>0},where the matrix A€ Rm×n is ill-conditioned,and there are errors in A and b.Besides overcoming the difficulties caused by ill-cond计ioning of the matrix A and errors in A and b,our method can also detect the infeasibility and the unboundedness of the polyhedral set P automatically during the compu tation.Det ailed mat hematical analyses for our method are presen ted and the worst case complexity of the algorithm is also given.Finally some numerical results are presented to show the robustness and effectiveness of the new method.
