In this article,we construct the most powerful family of simultaneous iterative method with global convergence behavior among all the existing methods in literature for finding all roots of non-linear equations.Conver...In this article,we construct the most powerful family of simultaneous iterative method with global convergence behavior among all the existing methods in literature for finding all roots of non-linear equations.Convergence analysis proved that the order of convergence of the family of derivative free simultaneous iterative method is nine.Our main aim is to check out the most regularly used simultaneous iterative methods for finding all roots of non-linear equations by studying their dynamical planes,numerical experiments and CPU time-methodology.Dynamical planes of iterative methods are drawn by using MATLAB for the comparison of global convergence properties of simultaneous iterative methods.Convergence behavior of the higher order simultaneous iterative methods are also illustrated by residual graph obtained from some numerical test examples.Numerical test examples,dynamical behavior and computational efficiency are provided to present the performance and dominant efficiency of the newly constructed derivative free family of simultaneous iterative method over existing higher order simultaneous methods in literature.展开更多
Herein,we propose a scheme for the realization of two-dimensional atomic localization in aλ-type three-level atomic medium such that the atom interacts with the two orthogonal standing-wave fields and a probe field.B...Herein,we propose a scheme for the realization of two-dimensional atomic localization in aλ-type three-level atomic medium such that the atom interacts with the two orthogonal standing-wave fields and a probe field.Because of the spatially dependent atom-field interaction,the information about the position of the atom can be obtained by monitoring the probe transmission spectra of the weak probe field for the first time.A single and double sharp localized peaks are observed in the one-wavelength domain.We have theoretically archived high-resolution and high-precision atomic localization within a region smaller thanλ/25×λ/25.The results may have potential applications in the field of nano-lithography and advance laser cooling technology.展开更多
基金the Natural Science Foundation of China(Grant Nos.61673169,11301127,11701176,11626101,and 11601485)The Natural Science Foundation of Huzhou City(Grant No.2018YZ07).
文摘In this article,we construct the most powerful family of simultaneous iterative method with global convergence behavior among all the existing methods in literature for finding all roots of non-linear equations.Convergence analysis proved that the order of convergence of the family of derivative free simultaneous iterative method is nine.Our main aim is to check out the most regularly used simultaneous iterative methods for finding all roots of non-linear equations by studying their dynamical planes,numerical experiments and CPU time-methodology.Dynamical planes of iterative methods are drawn by using MATLAB for the comparison of global convergence properties of simultaneous iterative methods.Convergence behavior of the higher order simultaneous iterative methods are also illustrated by residual graph obtained from some numerical test examples.Numerical test examples,dynamical behavior and computational efficiency are provided to present the performance and dominant efficiency of the newly constructed derivative free family of simultaneous iterative method over existing higher order simultaneous methods in literature.
基金supported by the Zhejiang Provincial Natural Science Foundation of China under Grant No.LD18A040001the National Key Research and Development Program of China(No.2017YFA0304202)the National Natural Science Foundation of China(Grant No.11974309)。
文摘Herein,we propose a scheme for the realization of two-dimensional atomic localization in aλ-type three-level atomic medium such that the atom interacts with the two orthogonal standing-wave fields and a probe field.Because of the spatially dependent atom-field interaction,the information about the position of the atom can be obtained by monitoring the probe transmission spectra of the weak probe field for the first time.A single and double sharp localized peaks are observed in the one-wavelength domain.We have theoretically archived high-resolution and high-precision atomic localization within a region smaller thanλ/25×λ/25.The results may have potential applications in the field of nano-lithography and advance laser cooling technology.
