Here presented is a matrix representation of recursive number sequences of order 3 defined by an = pa（n-1） ＋ qa（n-2） ＋ ra（n-3） with arbitrary initial conditions a0, a1 = 0, and a2 and their special cases of Pa...Here presented is a matrix representation of recursive number sequences of order 3 defined by an = pa（n-1） ＋ qa（n-2） ＋ ra（n-3） with arbitrary initial conditions a0, a1 = 0, and a2 and their special cases of Padovan number sequence and Perrin number sequence with initial conditions a0 = a1 = 0 and a2 = 1 and a0 = 3, a1 = 0, and a2 = 2, respectively. The matrix representation is used to construct many well known and new identities of recursive number sequences as well as Pavodan and Perrin sequences.展开更多
In this paper, we give precise formulas for the general two-dimensional recursion sequences by generating function method, and make use of the multivariate generating functions asymptotic estimation technique to compu...In this paper, we give precise formulas for the general two-dimensional recursion sequences by generating function method, and make use of the multivariate generating functions asymptotic estimation technique to compute their asymptotic values.展开更多
In this paper, the authors consider an adaptive recursive algorithm by selecting an adaptive sequence for computing M-estimators in multivariate linear regression models. Its asymptotic property is investigated. The r...In this paper, the authors consider an adaptive recursive algorithm by selecting an adaptive sequence for computing M-estimators in multivariate linear regression models. Its asymptotic property is investigated. The recursive algorithm given by Miao and Wu （1996） is modified accordingly. Simu- lation studies of the Mgorithm is also provided. In addition, the Newton-Raphson iterative algorithm is considered for the purpose of comparison.展开更多
The multivariate linearly recursive sequences have a long history and an immense range of application. Perterson and Taft first investigated the algebraic structure of linearly recursive sequences over a field under H...The multivariate linearly recursive sequences have a long history and an immense range of application. Perterson and Taft first investigated the algebraic structure of linearly recursive sequences over a field under Hurwitz product from the Hopf algebra point of view and these results are developed in ref. [2]. The present author also展开更多
It is proved that a linearly recursive sequence of n indices over field F (n≥1) is automatically a product of n linearly recursive sequences of 1-index over F by the theory of Hopf algebras.By the way, the correspond...It is proved that a linearly recursive sequence of n indices over field F (n≥1) is automatically a product of n linearly recursive sequences of 1-index over F by the theory of Hopf algebras.By the way, the correspondence between the set of linearly recursive sequences of 1-index and F[X]° is generalized to the case of n-index.展开更多
In this paper, we investigate the global behavior of a recursive sequence. We get sufficient conditions for the existence of the unique equilibrium point, and the unique equilibrium point is proved to be globally attr...In this paper, we investigate the global behavior of a recursive sequence. We get sufficient conditions for the existence of the unique equilibrium point, and the unique equilibrium point is proved to be globally attractive, also the attractive basin of the equilibrium is obtained.展开更多
In this paper, we study the global stability, and the periodic character of the rational recursive sequence. We show that the positive equilibrium of the sequence is a global attractor with a basin which depends on ce...In this paper, we study the global stability, and the periodic character of the rational recursive sequence. We show that the positive equilibrium of the sequence is a global attractor with a basin which depends on certain conditions posed on the coefficients.展开更多
We investigate the dynamics of two extensive classes of recursive sequences:Xn+1=c∑j=0^k(i0,i1…,i2j)∈A2j∑xn-i0xn-i1…xn-i2j+.f(xn-i0,xn-i1,...,xn-i2k)/c∑j=1^k(i0,i1,…,i2j-1)∈A2j-1∑xn-i0xn-i1…xn-i2j-1+c+f(xn-i...We investigate the dynamics of two extensive classes of recursive sequences:Xn+1=c∑j=0^k(i0,i1…,i2j)∈A2j∑xn-i0xn-i1…xn-i2j+.f(xn-i0,xn-i1,...,xn-i2k)/c∑j=1^k(i0,i1,…,i2j-1)∈A2j-1∑xn-i0xn-i1…xn-i2j-1+c+f(xn-i0,xn-i1,…,xn-i2k)and Xn+1c∑j=1^k(i0,i1,…,i2j-1)∈A2j-1∑xn-i0xn-i1…xn-i2j-1+c+f(xn-i0,xn-i1,…,xn-i2k)/c∑j=0^k(i0,i1…,i2j)∈A2j∑xn-i0xn-i1…xn-i2j+.f(xn-i0,xn-i1,...,xn-i2k)We prove that their unique positive equilibrium 5=1 is globally asymptotically stable.And a new access is presented to study the theory of recursive sequences.展开更多
文摘Here presented is a matrix representation of recursive number sequences of order 3 defined by an = pa（n-1） ＋ qa（n-2） ＋ ra（n-3） with arbitrary initial conditions a0, a1 = 0, and a2 and their special cases of Padovan number sequence and Perrin number sequence with initial conditions a0 = a1 = 0 and a2 = 1 and a0 = 3, a1 = 0, and a2 = 2, respectively. The matrix representation is used to construct many well known and new identities of recursive number sequences as well as Pavodan and Perrin sequences.
文摘In this paper, we give precise formulas for the general two-dimensional recursion sequences by generating function method, and make use of the multivariate generating functions asymptotic estimation technique to compute their asymptotic values.
基金supported by the National Natural Science Foundation for Young Scientists of China under Grant No.11101397the Natural Sciences and Engineering Research Council of Canada
文摘In this paper, the authors consider an adaptive recursive algorithm by selecting an adaptive sequence for computing M-estimators in multivariate linear regression models. Its asymptotic property is investigated. The recursive algorithm given by Miao and Wu （1996） is modified accordingly. Simu- lation studies of the Mgorithm is also provided. In addition, the Newton-Raphson iterative algorithm is considered for the purpose of comparison.
文摘The multivariate linearly recursive sequences have a long history and an immense range of application. Perterson and Taft first investigated the algebraic structure of linearly recursive sequences over a field under Hurwitz product from the Hopf algebra point of view and these results are developed in ref. [2]. The present author also
文摘It is proved that a linearly recursive sequence of n indices over field F (n≥1) is automatically a product of n linearly recursive sequences of 1-index over F by the theory of Hopf algebras.By the way, the correspondence between the set of linearly recursive sequences of 1-index and F[X]° is generalized to the case of n-index.
基金Research supported by Distinguished Expert Science Foundation of Naval Aeronautical and Astronautical University
文摘In this paper, we investigate the global behavior of a recursive sequence. We get sufficient conditions for the existence of the unique equilibrium point, and the unique equilibrium point is proved to be globally attractive, also the attractive basin of the equilibrium is obtained.
文摘In this paper, we study the global stability, and the periodic character of the rational recursive sequence. We show that the positive equilibrium of the sequence is a global attractor with a basin which depends on certain conditions posed on the coefficients.
基金Supported by the National Natural Science Foundation of China(Grant No10771169)
文摘We investigate the dynamics of two extensive classes of recursive sequences:Xn+1=c∑j=0^k(i0,i1…,i2j)∈A2j∑xn-i0xn-i1…xn-i2j+.f(xn-i0,xn-i1,...,xn-i2k)/c∑j=1^k(i0,i1,…,i2j-1)∈A2j-1∑xn-i0xn-i1…xn-i2j-1+c+f(xn-i0,xn-i1,…,xn-i2k)and Xn+1c∑j=1^k(i0,i1,…,i2j-1)∈A2j-1∑xn-i0xn-i1…xn-i2j-1+c+f(xn-i0,xn-i1,…,xn-i2k)/c∑j=0^k(i0,i1…,i2j)∈A2j∑xn-i0xn-i1…xn-i2j+.f(xn-i0,xn-i1,...,xn-i2k)We prove that their unique positive equilibrium 5=1 is globally asymptotically stable.And a new access is presented to study the theory of recursive sequences.
