The method of condition number is commonly used to diagnose a normal matrix N whether it is ill conditioned state or not.For its shortcoming,a method to measure multi collinearity of a matrix was put forward.The metho...The method of condition number is commonly used to diagnose a normal matrix N whether it is ill conditioned state or not.For its shortcoming,a method to measure multi collinearity of a matrix was put forward.The method is that implement Gram Schmidt orthogonalizing process to column vectors of a design matrix A(αl),then calculate the norms of every vector before and after orthogonalization process and their corresponding ratio,and use the minimum ratio among the group of ratios to measure the multi collinearity of A.According to the corresponding relationship between the multi collinearity and the ill conditioned state of a matrix,the method also studies and offers reference indexes weighing the ill conditioned state of a matrix based on the relative norm.The remarkable characteristics of the method are that the measure of multi collinearity has idiographic geometry meaning and clear lower and upper limit,the size of the measure reflects the multi collinearity of column vectors objectively.It is convenient to study the reason that results in the matrix being multi collinearity and to put forward solving plan according to the method which is summarized as the method of minimum norm and abbreviated as F method.展开更多
A disease transmission model of SEIR type is discussed in a stochastic point of view. We start by formulating the SEIR epidemic model in form of a system of nonlinear differential equations and then change it to a sys...A disease transmission model of SEIR type is discussed in a stochastic point of view. We start by formulating the SEIR epidemic model in form of a system of nonlinear differential equations and then change it to a system of nonlinear stochastic differential equations (SDEs). The numerical simulation of the resulting SDEs is done by Euler-Maruyama scheme and the parameters are estimated by adaptive Markov chain Monte Carlo and extended Kalman filter methods. The stochastic results are discussed and it is observed that with the SDE type of modeling, the parameters are also identifiable.展开更多
基金Project(40144018)supported by the National Natural Science Foundation of China
文摘The method of condition number is commonly used to diagnose a normal matrix N whether it is ill conditioned state or not.For its shortcoming,a method to measure multi collinearity of a matrix was put forward.The method is that implement Gram Schmidt orthogonalizing process to column vectors of a design matrix A(αl),then calculate the norms of every vector before and after orthogonalization process and their corresponding ratio,and use the minimum ratio among the group of ratios to measure the multi collinearity of A.According to the corresponding relationship between the multi collinearity and the ill conditioned state of a matrix,the method also studies and offers reference indexes weighing the ill conditioned state of a matrix based on the relative norm.The remarkable characteristics of the method are that the measure of multi collinearity has idiographic geometry meaning and clear lower and upper limit,the size of the measure reflects the multi collinearity of column vectors objectively.It is convenient to study the reason that results in the matrix being multi collinearity and to put forward solving plan according to the method which is summarized as the method of minimum norm and abbreviated as F method.
文摘A disease transmission model of SEIR type is discussed in a stochastic point of view. We start by formulating the SEIR epidemic model in form of a system of nonlinear differential equations and then change it to a system of nonlinear stochastic differential equations (SDEs). The numerical simulation of the resulting SDEs is done by Euler-Maruyama scheme and the parameters are estimated by adaptive Markov chain Monte Carlo and extended Kalman filter methods. The stochastic results are discussed and it is observed that with the SDE type of modeling, the parameters are also identifiable.
