摘要
To save the calculations of Jacobian,a multi-step Levenberg-Marquardt method named Shamanskii-like LM method for systems of nonlinear equations was proposed by Fa.Its convergence properties have been proved by using a trust region technique under the local error bound condition.However,the authors wonder whether the similar convergence properties are still true with standard line searches since the direction may not be a descent direction.For this purpose,the authors present a new nonmonotone m-th order Armijo type line search to guarantee the global convergence.Under the same condition as trust region case,the convergence rate also has been shown to be m+1 by using this line search technique.Numerical experiments show the new algorithm can save much running time for the large scale problems,so it is efficient and promising.
基金
supported by the Natural Science Foundation of Anhui Province under Grant No.1708085MF159
the Natural Science Foundation of the Anhui Higher Education Institutions under Grant Nos.KJ2017A375
KJ2019A0604
the abroad visiting of excellent young talents in universities of Anhui province under Grant No.GXGWFX2019022。
