fast algorithm for minimum norm direction of arrival estimation the original minimum norm direction of arrival estimator proposed by kumaresan and tufts employs the noise subspace projection matrix calculated by the eigendecomposition of spatial covariance matrix the present authors propose a novel noneigenvector fast algorithm which calculates the required minimum norm function using the special power basis instead of eigenvector basis the proposed algorithm provides a substantial saving as compared with computational loads of the eigendecomposition based minimum norm algorithm in cases when the number of multiple sources is much lower than the number of array sensors some computer simulation results verifying the high performance and accuracy of the proposed algorithm are presented

on the error estimates of several newton like methods1partial supported by the national natural science foundation of china and by natural science foundation of zhejiang province 1 in this paper convergence theorems and error estimates for several newton like iteration methods under new kantorovitch ostrowski type conditions using the information of higher derivatives at initial point s are established we get not only the convergence speed estimates of iterative sequence x n but also the estimates of f x n 1 f x n

relaxing convergence conditions for newton s method the classical kantorovich theorem on newton s method assumes that the first derivative of the operator involved satisfies a lipschitz condition 0 f x f y l x y in this paper we weaken this condition assuming that 0 f x f x0 x x0 for a given point x0

majorizing functions and two point newton type methods the semi local convergence of a newton type method used to solve nonlinear equations in a banach space is studied we also give as two important applications convergence analyses of two classes of two point newton type methods including a method mentioned in 5 and the midpoint method studied in 1 2 12 recently interest has been shown in such methods 3 4

a method for finding sharp error bounds for newton s method under the kantorovic assumptions this paper gives a method for finding sharpa posteriori error bounds for newton s method under the assumptions of kantorovich s theorem on the basis of this method new error bounds are derived and comparison is made among the known bounds of dennis 2 doring 4 gragg tapia 5 kantorovich 6 7 kornstaedt 9 lancaster 10 miel 11 13 moret 14 ostrowski 17 18 potra 19 and potra ptak 20

on newton s method under holder continuous derivative a mysovskii type theorem for newton s method under k p holder continuous derivative is considered in this paper for the application studied by others the new condition is weaker than ones in the literature also we prove that the optimal convergent order is p 1 for 0 p 1

newton method under weak lipschitz continuous derivative in banach spaces in the present paper a relax kantorovich type condition to guarantee the convergence of newton method with order 2 in banach space is obtained which takes the well known kantorovich and smale conditions as its special cases the relations between the new condition and the old ones are also studied

a new semilocal convergence theorem for newton s method abstract a new semilocal convergence theorem for newton s method is established for solving a nonlinear equation f x 0 defined in banach spaces it is assumed that the operator f is twice frechet differentiable and f satisfies a lipschitz type condition results on uniqueness of solution and error estimates are also given finally these results are compared with those that use kantorovich conditions

a newton type midpoint method with high efficiency index abstract in this paper we present a newton type two step method to approximate a solution of a nonlinear equation in banach spaces we establish a semilocal convergence theorem under newton kantorovich type conditions both the convergence order and the efficiency index of the developed method are found the iterative procedure presented here is a simple modification of the newton kantorovich method however with the same number of function and derivative evaluations at each iteration it is improved in two important aspects firstly the convergence order is increased from 2 for the newton kantorovich method to 1 2 2 414 for the new method secondly the efficiency index convergence order per function evaluation is improved from 2 1 414 to 1 2 1 2 1 553 we illustrate some of our results with a numerical example

on the semilocal convergence of efficient chebyshev secant type methods we introduce a three step chebyshev secant type method cstm with high efficiency index for solving nonlinear equations in a banach space setting we provide a semilocal convergence analysis for cstm using recurrence relations numerical examples validating our theoretical results are also provided in this study

two conditions concerning newton s method in this note we compare two conditions concerning newton s method and find out that even under some weaker condition one has the convergence of the newton s method and a better error bound than the relative strong condition

on a theorem of l v kantorovich concerning newton s method we study the problem of approximating a locally unique solution of an operator equation using newton s method the well known convergence theorem of l v kantorovich involves a bound on the second frechet derivative or the lipschitz frechet differentiability of the operator involved on some neighborhood of the starting point here we provide local and semilocal convergence theorems for newton s method assuming the frechet differentiability only at a point which is a weaker assumption a numerical example is provided to show that our result can apply to solve a scalar equation where the above mentioned ones may not

starting points for newton s method under a center lipschitz condition for the second derivative abstract we analyze the semilocal convergence of newton s method under a center lipschitz condition for the second derivative of the operator involved different from that used by other authors until now in particular we propose to center the lipschitz condition for the second derivative in a different point from that where newton s method starts this allows us to obtain different starting points for newton s method and modify the domain of starting points

a new semilocal convergence theorem for newton s method in banach space using hypotheses on the second frechet derivative a new global kantorovich type convergence theorem for newton s method in banach space is provided for approximating a solution of a nonlinear equation it is assumed that a solution exists and the second frechet derivative of the operator involved satisfies a lipschitz condition our convergence condition differs from earlier ones and therefore it has theoretical and practical value finally a simple numerical example is provided to show that our results apply where earlier ones fail

a new semilocal convergence theorem for newton s method involving twice frechet differentiability at only one point in this study we provide a new semilocal convergence theorem for newton s method it is assumed that an operator is twice continuously frechet differentiable at only one point finally a simple numerical example is given to show that our results can apply but earlier similar ones fail

extending the newton kantorovich hypothesis for solving equations the famous newton kantorovich hypothesis kantorovich and akilov 1982 3 argyros 2007 2 argyros and hilout 2009 7 has been used for a long time as a sufficient condition for the convergence of newton s method to a solution of an equation in connection with the lipschitz continuity of the frechet derivative of the operator involved here using lipschitz and center lipschitz conditions and our new idea of recurrent functions we show that the newton kantorovich hypothesis can be weakened under the same information moreover the error bounds are tighter than the corresponding ones given by the dominating newton kantorovich theorem argyros 1998 1 2 7 ezquerro and hernandez 2002 11 3 proinov 2009 2010 16 17 numerical examples including a nonlinear integral equation of chandrasekhar type chandrasekhar 1960 9 as well as a two boundary value problem with a green s kernel argyros 2007 2 are also provided in this study

indices of convexity and concavity application to halley method we define an index to measure the convexity of a convex function f at each point we use this index to establish conditions on the convergence of the halley method in the complex plane and in banach spaces

a note on the kantorovich theorem for newton iteration abstract in this paper a new theorem for the newton method convergence is obtained its condition is different from that of the kantorovich theorem and therefore it has theoretical and practical value

a newton kantorvich theorem for equations involving m frechet differentiable operators and applications in radiative transfer abstract in this study we approximate a locally unique solution of a nonlinear operator equation in banach space using newton s method a complete error analysis showing the quadratic convergence of our method is also given our new theorem uses lipschitz or holder continuity assumptions on m frechet differentiable operators where m 2 is a positive integer a numerical example is given to show that our results provide a better information on the location of the solution as well as finer error bounds on the distances involved than earlier results a second numerical example shows how to solve a nonlinear integral equation appearing in radiative transfer

third order convergence theorem by using majorizing function for a modified newton method in banach space abstract following the ideas of frontini and sormani we present a modified newton method in banach space which is used to solve the nonlinear operator equation we establish the newton kantorovich convergence theorem for the modified newton method with third order convergence in banach space by using majorizing function we also get the error estimate finally two examples are provided to show the application of our theorem

weak convergence conditions for inexact newton type methods abstract we establish a new semilocal convergence results for inexact newton type methods for approximating a locally unique solution of a nonlinear equation in a banach spaces setting we show that our sufficient convergence conditions are weaker and the estimates of error bounds are tighter in some cases than in earlier works 15 31 special cases and numerical examples are also provided in this study

on newton s method for solving equations containing frechet differentiable operators of order at least two we provide sufficient conditions for the semilocal convergence of newton s method to a locally unique solution of a nonlinear operator equation containing operators that are frechet differentiable of order at least two in a banach space setting numerical examples are also provided to show that our results apply to solve nonlinear equations in cases earlier ones cannot j m gutierrez a new semilocal convergence theorem for newton s method j comput appl math 79 1997 131 145 z huang a note of kantorovich theorem for newton iteration j comput appl math 47 1993 211 217 f a potra sharp error bounds for a class of newton like methods libertas mathematica 5 1985 71 84

weak convergence conditions for the newton s method in banach space using general majorizing sequences using the majorizing principle we develop sufficient convergence conditions for the semilocal convergence of newton s method in a banach space setting the involved majorizing sequences are very general and as special cases include most relevant sequences from the published literature our convergence conditions can be weaker and our error analysis can be finer than before

on the local convergence of fast two step newton like methods for solving nonlinear equations a local convergence analysis is presented for a fast two step newton like method tsnlm for solving nonlinear equations in a banach space setting the tsnlm unifies earlier methods such as newton s secant newton like chebyshev secant chebyshev newton steffensen stirling s and other single or multistep methods numerical examples and a comparative study of these methods validating our theoretical results are also given in the concluding section of this paper

extending the domain of starting points for newton s method under conditions on the second derivative abstract in this paper we propose a center lipschitz condition for the second frechet derivative together with the use of restricted domains in order to improve the domain of starting points for newton s method in addition we compare the new result with an older one and see that the former improves the latter