SINCE there are many difficulties in finding a single root of a polynomial, it becomes moreand more important for parallel iterations to determine all roots simultaneously. Among theproposed methods, the iterative fam...SINCE there are many difficulties in finding a single root of a polynomial, it becomes moreand more important for parallel iterations to determine all roots simultaneously. Among theproposed methods, the iterative fami1y produced by paralleling the iterative family of Halleyusing Bell’s polynomial appears the most systematic and richest. In fact the paper becomesthe main contents of the monograph.展开更多
Presents a family of parallel iterations for finding all zeros of a polynomial without evaluation of derivatives. Construction of iterations; Convergence of the iterations; Details on the numerical examples.
Presents the first estimation conditions for Nourein iterations for simultaneous finding all zeros of a polynomial under which the iteration processes are guaranteed to converge. Computational formulas; Theorems and p...Presents the first estimation conditions for Nourein iterations for simultaneous finding all zeros of a polynomial under which the iteration processes are guaranteed to converge. Computational formulas; Theorems and proofs.展开更多
In this paper it is shown m two different ways that one of the family of parallel iterations to determine all real quadratic factors of polynomials presented in [12] is Newton's method applied to the special equat...In this paper it is shown m two different ways that one of the family of parallel iterations to determine all real quadratic factors of polynomials presented in [12] is Newton's method applied to the special equation (1.7) below. Furthermore, we apply Chebyshev's method to (1.7) and obtain a new parallel iteration for factorization of polynomials. Finally, some properties of the parallel iterations are discussed.展开更多
A class of asynchronous nested matrix multisplitting methods for solving large-scale systems of linear equations are proposed, and their convergence characterizations are studied in detail when the coefficient matrice...A class of asynchronous nested matrix multisplitting methods for solving large-scale systems of linear equations are proposed, and their convergence characterizations are studied in detail when the coefficient matrices of the linear systems are monotone matrices and H-matrices, respectively.展开更多
For a class of ideal models of parallel computers, we define some measuring parameters such as the speed-up, the efficiency, the redundancy of a linear and nonlinear parallel iteration method in both average and asymp...For a class of ideal models of parallel computers, we define some measuring parameters such as the speed-up, the efficiency, the redundancy of a linear and nonlinear parallel iteration method in both average and asymptotic senses, as well as the utilization ratio of the parallel computer. These parameters are reasonable and convenient for the theoretical studies of the parallel iteration methods.展开更多
基金This paper is partially supported by the Bulgarian Mutistry of Education SciencesTechnologies Project MM-515/97+1 种基金partially supported by the National Natural Science Foundation of Chinaby Natu-ral Science Foundation of Zhejiang Province.
文摘In this paper we consider some parallel iterations for splitting quadratic factors of polynomials and their convergence.
文摘SINCE there are many difficulties in finding a single root of a polynomial, it becomes moreand more important for parallel iterations to determine all roots simultaneously. Among theproposed methods, the iterative fami1y produced by paralleling the iterative family of Halleyusing Bell’s polynomial appears the most systematic and richest. In fact the paper becomesthe main contents of the monograph.
基金National Natural Science Foundation of ChinaNatural Science Foundation of Zhejiang Province
文摘Presents a family of parallel iterations for finding all zeros of a polynomial without evaluation of derivatives. Construction of iterations; Convergence of the iterations; Details on the numerical examples.
基金National Natural Science Foundation of China Natural ScienceFoundation of Zhejiang Province.
文摘Presents the first estimation conditions for Nourein iterations for simultaneous finding all zeros of a polynomial under which the iteration processes are guaranteed to converge. Computational formulas; Theorems and proofs.
基金The Project Supported by National Natural Science Foundation of China and by Natural Science Foundation of Zhejiang Province.
文摘In this paper it is shown m two different ways that one of the family of parallel iterations to determine all real quadratic factors of polynomials presented in [12] is Newton's method applied to the special equation (1.7) below. Furthermore, we apply Chebyshev's method to (1.7) and obtain a new parallel iteration for factorization of polynomials. Finally, some properties of the parallel iterations are discussed.
文摘A class of asynchronous nested matrix multisplitting methods for solving large-scale systems of linear equations are proposed, and their convergence characterizations are studied in detail when the coefficient matrices of the linear systems are monotone matrices and H-matrices, respectively.
文摘For a class of ideal models of parallel computers, we define some measuring parameters such as the speed-up, the efficiency, the redundancy of a linear and nonlinear parallel iteration method in both average and asymptotic senses, as well as the utilization ratio of the parallel computer. These parameters are reasonable and convenient for the theoretical studies of the parallel iteration methods.
