A(n,k)=sum from m=1 to k sum r=1 to m sum j=0 to [k/m]-1 (tm,r,j (k)×nj×s(r,m)×ζmnr,ζm=e2πi/m,s(r,m)={1,gcd(r,m)=1 0,其他)为丢番图方程sum i=1 to k (ixi=n)的非负整数解的个数.虽然用解线性方程组的方法...A(n,k)=sum from m=1 to k sum r=1 to m sum j=0 to [k/m]-1 (tm,r,j (k)×nj×s(r,m)×ζmnr,ζm=e2πi/m,s(r,m)={1,gcd(r,m)=1 0,其他)为丢番图方程sum i=1 to k (ixi=n)的非负整数解的个数.虽然用解线性方程组的方法可求得A(n,k)的所有系数,然而,该求解过程却非常耗时.本文利用方程(1-x)(1-x2)...(1-xk)=0的相异根的幂可能存在的相等关系,即取适当的正整数g使某些相异根的g次幂相等来实现同类项系数的合并以降低方程的维数,达到提高方程求解速度的目的.展开更多
In this paper, a new step-size skill for a projection and contraction method([10]) for linear programming is generalized to an iterative method([22]) for solving nonlinear projection equation. For linear programming, ...In this paper, a new step-size skill for a projection and contraction method([10]) for linear programming is generalized to an iterative method([22]) for solving nonlinear projection equation. For linear programming, our scheme is the same as that of([10]). For complementarity problem and related problems, we give an improved algorithm by considering the new step-size skill and ALGORITHM B discussed in [22]. Numerical results are provided.展开更多
A method for solving nonlinear polynomial equations is given which avoids theappearance of redundant factors as in the previous characteristic set method developed bythe present author. The new method seems thus to be...A method for solving nonlinear polynomial equations is given which avoids theappearance of redundant factors as in the previous characteristic set method developed bythe present author. The new method seems thus to be of much higher efficiency than theprevious one. It has the further advantage that numerical data may be inserted at willeither at the outset or during the procedure so far removal of factors by divisions may beavoided.展开更多
文摘A(n,k)=sum from m=1 to k sum r=1 to m sum j=0 to [k/m]-1 (tm,r,j (k)×nj×s(r,m)×ζmnr,ζm=e2πi/m,s(r,m)={1,gcd(r,m)=1 0,其他)为丢番图方程sum i=1 to k (ixi=n)的非负整数解的个数.虽然用解线性方程组的方法可求得A(n,k)的所有系数,然而,该求解过程却非常耗时.本文利用方程(1-x)(1-x2)...(1-xk)=0的相异根的幂可能存在的相等关系,即取适当的正整数g使某些相异根的g次幂相等来实现同类项系数的合并以降低方程的维数,达到提高方程求解速度的目的.
文摘In this paper, a new step-size skill for a projection and contraction method([10]) for linear programming is generalized to an iterative method([22]) for solving nonlinear projection equation. For linear programming, our scheme is the same as that of([10]). For complementarity problem and related problems, we give an improved algorithm by considering the new step-size skill and ALGORITHM B discussed in [22]. Numerical results are provided.
基金The present project is partially supported by NSFC Grant JI85312.
文摘A method for solving nonlinear polynomial equations is given which avoids theappearance of redundant factors as in the previous characteristic set method developed bythe present author. The new method seems thus to be of much higher efficiency than theprevious one. It has the further advantage that numerical data may be inserted at willeither at the outset or during the procedure so far removal of factors by divisions may beavoided.
