Making use of the theory of continuous homotopy and the relation betweensymmetric polynomtal and polynomtal in one variable the arthors devoted ims article to constructing a regularly homotopic curve with probability ...Making use of the theory of continuous homotopy and the relation betweensymmetric polynomtal and polynomtal in one variable the arthors devoted ims article to constructing a regularly homotopic curve with probability one. Discrete tracingalong this honlotopic curve leads 10 a class of Durand-Kerner algorithm with stepparameters. The convergernce of this class of algorithms is given, which solves theconjecture about the global property of Durand-Kerner algorithm. The.problem forsteplength selection is thoroughly discussed Finally, sufficient numerical examples areused to verify our theory展开更多
Kerner pointed that the sequence (x1m,x2m,…xnm)converges to （r1,r2,…rn）（m→∞）if the initial approximation (x10, x20, …, xn（0）) is close to （r1, r2,…rn） sufficiently. The convergence of(x1m, x2m,…, xnm) p...Kerner pointed that the sequence (x1m,x2m,…xnm)converges to （r1,r2,…rn）（m→∞）if the initial approximation (x10, x20, …, xn（0）) is close to （r1, r2,…rn） sufficiently. The convergence of(x1m, x2m,…, xnm) produced by （2） from (x10,x20,…,xn（0）) usually cannot be testified because （r1, r2,…,rn） is unknown. The purpose of this paper is to give sufficient conditions for testifying the convergence.展开更多
In this paper we propose the two kinds of different criterions and use them to judge the convergence of Durand-Kerner method and to compare the obtained results with other methods. [ABSTRACT FROM AUTHOR]
文摘Making use of the theory of continuous homotopy and the relation betweensymmetric polynomtal and polynomtal in one variable the arthors devoted ims article to constructing a regularly homotopic curve with probability one. Discrete tracingalong this honlotopic curve leads 10 a class of Durand-Kerner algorithm with stepparameters. The convergernce of this class of algorithms is given, which solves theconjecture about the global property of Durand-Kerner algorithm. The.problem forsteplength selection is thoroughly discussed Finally, sufficient numerical examples areused to verify our theory
文摘Kerner pointed that the sequence (x1m,x2m,…xnm)converges to （r1,r2,…rn）（m→∞）if the initial approximation (x10, x20, …, xn（0）) is close to （r1, r2,…rn） sufficiently. The convergence of(x1m, x2m,…, xnm) produced by （2） from (x10,x20,…,xn（0）) usually cannot be testified because （r1, r2,…,rn） is unknown. The purpose of this paper is to give sufficient conditions for testifying the convergence.
基金National 973 Fundamental Research Project of China and Provincial NaturalScience Foundation.
文摘In this paper we propose the two kinds of different criterions and use them to judge the convergence of Durand-Kerner method and to compare the obtained results with other methods. [ABSTRACT FROM AUTHOR]
