generalized iterative process and associated regularization for j pseudomonotone mixed variational inequalities a generalized iterative process for solving mixed variational inequalities with j pseudomonotone operators in uniformly smooth banach spaces is proposed and its weak convergence is established an application to the stationary filtration problem is given for such variational inequalities a generalized iterative regularization method is constructed and its weak convergence under the assumption that the iterative parameter may vary from step to step is analyzed our results extend and generalize the corresponding theorems of a m saddeek s a ahmed convergence analysis of iterative methods for some variational inequalities with j pseudomonotone operators in uniformly smooth banach spaces appl sci comput accepted for publication a m saddeek s a ahmed on the convergence of some iteration processes for j pseudomonotone mixed variational inequalities in uniformly smooth banach spaces math comput modell 46 3 4 2007 557 572

a general and exact method for determining limit cycles in decentralized relay systems an exact method for evaluating the periods and stability of limit cycles in decentralized relay systems is presented the method can cope with relays having dead zones and hystereses the underlying idea is to convert the continuous decentralized relay system under a limit cycle to an equivalent fictitious sampled data system with synchronous samplers consequently regular sampled data tools can be applied in a straightforward manner to derive closed form necessary conditions as well as stability conditions and other properties of such systems this paper extends and generalises recent results obtained by the authors

on the steepest descent approximation method for the zeros of generalized accretive operators abstract in this paper we present certain characteristic conditions for the convergence of the generalized steepest descent approximation process to a zero of a generalized strongly accretive operator defined on a uniformly smooth banach space our study is based on an important result of reich s reich an iterative procedure for constructing zeros of accretive sets in banach spaces nonlinear anal 2 1978 85 92 and given results extend and improve some of the earlier results which include the steepest descent approximation method

iterative process with errors of nonlinear equations involvingm accretive operators abstract let x be a uniformly smooth and uniformly convex banach space and t d t x x be an m accretive operator with the domain d t and the range r t for any given f x we prove that the mann and ishikawa type iterative sequences with errors converge strongly to the unique solution of the equation x tx f where t may not be lipschitz some related results deal with the convergence of mann and ishikawa type iterative sequences with errors for approximating a solution of a continuous dissipative operator equation

picard iterations for solution of nonlinear equations in certain banach spaces abstract let e be a real uniformly smooth banach space and let a d a e e be locally lipschitzian and strongly quasi accretive it is proved that a picard recursion process converges strongly to the unique solution of the equation ax f f r a with the convergence being at least as fast as a geometric progression related results deal with the convergence of picard iterations to the fixed point of locally lipschitzian strong hemicontractions t and to the solutions of nonlinear equations of the forms x ax f and x ax f where a is an accretive type map

iterative solution of nonlinear equations of accretive and pseudocontractive types abstract let e be a real uniformly smooth banach space let a d a e 2 e be an accretive operator that satisfies the range condition and a 1 0 let n and n be two real sequences satisfying appropriate conditions and for z e arbitrary let the sequence x n be generated from arbitrary x 0 e by x n 1 x n n u n n x n z u n ax n n 0 assume that u n is bounded it is proved that x n converges strongly to some x a 1 0 furthermore if k is a nonempty closed convex subset of e and t k k is a bounded continuous pseudocontractive map with f t tx x it is proved that for arbitrary z k the sequence x n generated from x 0 k by x n 1 x n n i t x n n x n z n 0 where n and n are real sequences satisfying appropriate conditions converges strongly to a fixed point of t

some problems and results in the study of nonlinear analysis this paper is presented as a survey of the latest and new results on some topics in the study of nonlinear analysis which were obtained by the author and some chinese mathematicians

existence of solutions and convergence of iterative algorithms for a system of generalized nonlinear mixed quasi variational inclusions in this paper we introduce and study a new system of generalized nonlinear mixed quasi variational inclusions in q uniformly smooth banach spaces we prove the existence and uniqueness of solutions for this system of generalized nonlinear mixed quasi variational inclusions we also prove the convergence of several new two step iterative algorithms with or without errors for this system of generalized nonlinear mixed quasi variational inclusions the results in this paper extend and improve some known results in the literature

a generalized steepest descent approximation for the zeros of m accretive operators a necessary and sufficient condition is proved for a generalized steepest descent approximation to converge to the zeros of m accretive operators related results deal with the convergence of the scheme to fixed points of pseudocontractive maps

limit cycles in decentralized relay systems abstract the problem of limit cycles in decentralized relay systems is revisited an exact method for evaluating the periods of limit cycles and determining their stability in such systems is presented though the necessary conditions derived in this paper are equivalent to the existing and well known infinite series counterpart conditions the new conditions are constructive and easier to apply since they are given in closed form the new method is applicable to any system and uses the z transform familiar to most control engineers and for which extensive tables can be found in most textbooks on discrete time control examples demonstrate the usefulness of the new conditions the new method also reveals an interesting property of decentralized relay systems

iterative solution of nonlinear equations involving set valued uniformly accretive operators abstract let e be a real normed linear space and let a e 2 e be a uniformly continuous and uniformly quasi accretive multivalued map with nonempty closed values such that the range of i a is bounded and the inclusion f ax has a solution x e it is proved that ishikawa and mann type iteration processes converge strongly to x further if t e 2 e is a uniformly continuous and uniformly hemicontractive set valued map with bounded range and a fixed point x e it is proved that both the mann and ishikawa type iteration processes converge strongly to x the strong convergence of these iteration processes with errors is also proved

strong convergence theorems for finitely many nonexpansive mappings and applications abstract let e be a uniformly convex banach space which satisfies opial s condition or whose norm is frechet differentiable recently takahashi and shimoji w takahashi k shimoji convergence theorems for nonexpansive mappings and feasibility problems math comput modelling 32 2000 1463 1471 introduced an iterative scheme given by finitely many nonexpansive mappings in e and proved weak convergence theorems which are connected with the problem of image recovery in this paper we introduce a new iterative scheme which includes their iterative scheme as a special case under the assumption that e is a reflexive banach space whose norm is uniformly g teaux differentiable and which has a weakly continuous duality mapping we prove strong convergence theorems which are connected with the problem of image recovery using the established results we consider the problem of finding a common fixed point of finitely many nonexpansive mappings

approximate inference for disease mapping with sparse gaussian processes gaussian process gp models are widely used in disease mapping as they provide a natural framework for modeling spatial correlations their challenges however lie in computational burden and memory requirements in disease mapping models the other difficulty is inference which is analytically intractable due to the non gaussian observation model in this paper we address both these challenges we show how to efficiently build fully and partially independent conditional fic pic sparse approximations for the gp in two dimensional surface and how to conduct approximate inference using expectation propagation ep algorithm and laplace approximation la we also propose to combine fic with a compactly supported covariance function to construct a computationally efficient additive model that can model long and short length scale spatial correlations simultaneously the benefit of these approximations is computational the sparse gps speed up the computations and reduce the memory requirements the posterior inference via ep and laplace approximation is much faster and is practically as accurate as via markov chain monte carlo

on the asymptotic behavior of nonlinear semigroups and the range of accretive operators ii abstract it is known that certain problems in partial differential equations may be interpreted as initial value problems for ordinary differential equations in banach spaces when such an evolution equation is governed by an accretive operator then its solutions give rise to a nonlinear contraction semigroup in this paper we study certain aspects of the asymptotic behavior of nonlinear semigroups and or resolvents of accretive operators we also derive new results on their behavior at the origin it turns out that the behavior of a nonlinear semigroup resembles that of the resolvent of its generator both at infinity and at the origin author

approximation of solutions of generalized equations of hammerstein type let h be a real hilbert space for each i 1 2 m let f i k i h h be bounded and monotone mappings assume that the generalized hammerstein equation u i 1 mk if iu 0 has a solution in h we construct a new explicit iterative sequence and prove strong convergence of the sequence to a solution of the generalized hammerstein equation

error bounds for approximation solutions to nonlinear equations of strongly accretive operators in uniformly smooth banach spaces abstract let x be a uniformly smooth banach space and t x x a strongly accretive operator in this paper we give the error bounds for the approximation solutions of the nonlinear equation tx f generated by both the mann and the ishikawa iteration process on the other hand let k be a nonempty convex subset of x and t k k a strictly pseudocontractive mapping the related results deal with the error bounds for the iterative approximation of the fixed point of t generated by these two processes

convergence and almost stability of ishikawa iterative scheme with errors for m accretive operators let x be a uniformly smooth real banach space and t x x be a generalized lipschitzian and m accretive operator it is proved that under suitable conditions the ishikawa iterative schemes with errors both converges strongly to the unique solution of the nonlinear operator equation x tx f and is almost stable a few related results deal with the operator equations for the dissipative type operator the results presented in this paper extend substantially the corresponding results in 1 2

the solution by iteration of nonlinear equations in uniformly smooth banach spaces abstract letebe a uniformly smooth banach space and lett d t e ebe a strong pseudocontraction with an open domaind t ineand a fixed pointx d t we establish the strong convergence of the mann and ishikawa iterative processes with errors to the fixed point oft related results deal with the iterative solution of operator equations of the formsf txandf x tx 0 whentis a set valued strongly accretative operator our theorems include the cases in which the operatortis defined only locally explicit error estimates are also given

an analysis of a multi level projected steepest descent iteration for nonlinear inverse problems in banach spaces subject to stability constraints we consider nonlinear inverse problems described by operator equations in banach spaces assuming conditional stability of the inverse problem that is assuming that stability holds on a compact convex subset of the domain of the operator we introduce a novel nonlinear projected steepest descent iteration and analyze its convergence to an approximate solution given limited accuracy data we proceed with developing a multi level algorithm based on a nested family of compact convex subsets on which stability holds and the stability constants are ordered growth of the stability constants is coupled to the increase in accuracy of approximation between neighboring levels to ensure that the algorithm can continue from level to level until the iterate satisfies a desired discrepancy criterion after a finite number of steps

prox regular sets and epigraphs in uniformly convex banach spaces various regularities and other properties we continue the study of prox regular sets that we began in a previous work in the setting of uniformly convex banach spaces endowed with a norm both uniformly smooth and uniformly convex e g l p w m p spaces we prove normal and tangential regularity properties for these sets and in particular the equality between mordukhovich and proximal normal cones we also compare in this setting the proximal normal cone with different holderian normal cones depending on the power types s q of moduli of smoothness and convexity of the norm in the case of sets that are epigraphs of functions we show that j primal lower regular functions have prox regular epigraphs and we compare these functions with poliquin s primal lower nice functions depending on the power types s q of the moduli the preservation of prox regularity of the intersection of finitely many sets and of the inverse image is obtained under a calmness assumption a conical derivative formula for the metric projection mapping of prox regular sets is also established among other results of the paper it is proved that the attouch wets convergence preserves the uniform r prox regularity property and that the metric projection mapping is in some sense continuous with respect to this convergence for such sets

strong convergence theorem for approximation of solutions of equations of hammerstein type abstract let h be a real hilbert space let k f h h be bounded continuous and monotone mappings suppose that u h is a solution to the hammerstein equation u k f u 0 we construct a new explicit iterative sequence and prove strong convergence of the sequence to a solution of the hammerstein equation furthermore we give some examples to show that our result is interdisciplinary in nature covers a large variety of areas and should be of much interest to a wide audience

on computing inverse entries of a sparse matrix in an out of core environment the inverse of an irreducible sparse matrix is structurally full so that it is impractical to think of computing or storing it however there are several applications where a subset of the entries of the inverse is required given a factorization of the sparse matrix held in out of core storage we show how to compute such a subset e ciently by accessing only parts of the factors when there are many inverse entries to compute we need to guarantee that the overall computation scheme has reasonable memory requirements while minimizing the cost of loading the factors this leads to a partitioning problem that we prove is np complete we also show that we cannot get a close approximation to the optimal solution in polynomial time we thus need to develop heuristic algorithms and we propose i a lower bound on the cost of an optimum solution ii an exact algorithm for a particular case iii two other heuristics for a more general case and iv hypergraph partitioning models for the most general setting we illustrate the performance of our algorithms in practice using the mumps software package on a set of real life problems as well as some standard test matrices we show that our techniques can improve the execution time by a factor of 50 key words sparse matrices direct methods for linear systems and matrix inversion multifrontal method graphs and hypergraphs

an auto tuner for smith dead time compensator an efficient yet simple automatic tuning algorithm is developed for dead time compensators dtc common to industrial process controllers the auto tuner is capable of setting eight tuning parameters two for the primary controller three for the process model and another three for an additional modification aimed at improving the disturbance rejection properties the process model used in the algorithm is a first order dead time which captures the essential dynamics of the majority of loops in the chemical and process industries the methodology and methods used however can be readily extended to higher order and more complicated models the auto tuner utilizes two points on the process nyquist curve acquired through automatically generated controlled limit cycles in closed loop fashion least squares is then used to estimate the process model it is shown that an appropriate selection of the two points as well as the weighting matrix in the least squares leads to a robust estimation a simple rule b

analysis of second order sliding mode algorithms in the frequency domain a frequency domain analysis of the second order sliding mode algorithms particularly of the twisting algorithm is carried out in the frequency domain with the use of the describing function method and tsypkin s approach it is shown that in the presence of an actuator the transient process may converge to a periodic motion parameters of this periodic motion are analyzed a comparison of the periodic solutions in the systems with higher order sliding mode controllers and the oscillations that occur in classical sliding mode systems with actuators is done

on a new system of generalized mixed quasi variational like inclusions involving a η m accretive operators with applications in this paper we introduce a new and interesting system of generalized mixed quasi variational like inclusions with a h m accretive operators and relaxed cocoercive mappings which contains variational inequalities variational inclusions systems of variational inequalities systems of variational like inequalities and systems of variational inclusions in the literature as special cases by using the resolvent technique for the a h m accretive operators we prove the existence of solutions and the convergence of a new p step iterative algorithm for this system of generalized mixed quasi variational like inclusions in real q uniformly smooth banach spaces the results in this paper unifies extends and improves some known results in the literature

local stability of limit cycles for mimo relay feedback systems abstract this paper concerns with the local stability of limit cycles for decentralized relay feedback systems it presents a sufficient condition for the local stability based on the well known poincare map method the effectiveness of the presented result is illustrated by a numerical example

differentiation of matrix functionals using triangular factorization in various applications it is necessary to differentiate a matrix functional w a x where a x is a matrix depending on a parameter vector x usually the functional itself can be readily computed from a triangular factorization of a x this paper develops several methods that also use the triangular factorization to efficiently evaluate the first and second derivatives of the functional both the full and sparse matrix situations are considered there are similarities between these methods and algorithmic differentiation however the methodology developed here is explicit leading to new algorithms it is shown how the methods apply to several applications where the functional is a log determinant including spline smoothing covariance selection and restricted maximum likelihood

strong convergence theorem for integral equations of hammerstein type in hilbert spaces let h be a real hilbert space let f h h be a bounded coercive and maximal monotone mapping let k h h be a bounded and maximal monotone mapping let k and f satisfy the range condition suppose that u h is a solution to hammerstein equation u kfu 0 we construct a new explicit iterative sequence and prove strong convergence of the sequence to a solution of the hammerstein equation our iterative scheme in this paper seems far simpler than the iterative scheme used by chidume and ofoedu 2011 13 and their strong assumption is dispensed with we give some examples of our result so that it will find serious applications and be of much interest to our readers

the learning rate of lp coefficient regularized shannon sampling algorithm in the present paper we provide an investigation on the learning rate of the shannon sampling algorithms with l p coefficient regularization we give the upper bounds for the sample error and the regularization error with the convex inequality in l p spaces and show the approximation error by a k functional whose convergence rate can be sum up to the translation network approximation basing on these estimates we show an explicit learning rate in possibility

the viscosity approximation method for asymptotically nonexpansive mappings in banach spaces abstract a recent trend in the iterative methods for constructing fixed points of nonlinear mappings is to use the viscosity approximation technique the advantage of this technique is that one can find a particular solution to the associated problems and in most cases this particular solution solves some variational inequality in this paper we try to extend this technique to find a particular common fixed point of a finite family of asymptotically nonexpansive mappings in a banach space which is reflexive and has a weakly continuous duality map both implicit and explicit viscosity approximation schemes are proposed and their strong convergence to a solution to a variational inequality is proved

viscosity approximation to common fixed points of families of nonexpansive mappings with generalized contractions mappings abstract let x be a reflexive and smooth real banach space which has a weakly sequentially continuous duality mapping in this paper we consider the following viscosity approximation scheme x n 1 n 1 f x n 1 n 1 t n 1 x n where f is a generalized contraction mapping for infinitely many nonexpansive self mappings t 1 t 2 t 3 in x we establish a strong convergence result which generalizes some results in the literature

steepest descent method for equilibrium points of nonlinear systems with accretive operators let e be a real normed linear space and let a e 2e be a bounded uniformly continuous strongly accretive multi valued map with nonempty closed values such that the inclusion 0 ax has a solution x e it is proved that both the ishikawa and the mann iteration processes are bounded and converge strongly to x related results deal with the convergence of the iteration processes to fixed points of strongly pseudocontractive maps and the iterative solution of the equation 0 x fx for an accretive map f furthermore the ishikawa and mann iteration methods with errors are discussed and proofs are sketched on how our theorems extend to these methods our method of proof is of independent interest

on the iteratively regularized gauss newton method in banach spaces with applications to parameter identification problems in this paper we propose an extension of the iteratively regularized gauss newton method to the banach space setting by defining the iterates via convex optimization problems we consider some a posteriori stopping rules to terminate the iteration and present the detailed convergence analysis the remarkable point is that in each convex optimization problem we allow non smooth penalty terms including l 1 and total variation like penalty functionals this enables us to reconstruct special features of solutions such as sparsity and discontinuities in practical applications some numerical experiments on parameter identification in partial differential equations are reported to test the performance of our method

proximal normal cone analysis on smooth banach spaces and applications unlike the frechet penot clarke and other order one notions of normal cones the notion of proximal normal cone describes variational behavior of order two and most of results on proximal normal cone are established in the hilbert space framework a possible reason is that in a general banach space such as in the classical banach spaces l p and l p with 1 leq p 2 the proximal normal cone of a smooth subset a at every point of a may consist of the zero element only nevertheless on the other hand we show in this paper that for a fairly big class of smooth banach spaces including the classical banach spaces l p and l p with 2 leq p infty the consideration of proximal normal cones provides a lot of useful information especially for leading to satisfactory treatment for constrained optimization problems some of our results are new even in the hilbert space case

a hybrid method for the parallel computation of green s functions quantum transport models for nanodevices using the non equilibrium green s function method require the repeated calculation of the block tridiagonal part of the green s and lesser green s function matrices this problem is related to the calculation of the inverse of a sparse matrix because of the large number of times this calculation needs to be performed this is computationally very expensive even on supercomputers the classical approach is based on recurrence formulas which cannot be efficiently parallelized this practically prevents the solution of large problems with hundreds of thousands of atoms we propose new recurrences for a general class of sparse matrices to calculate green s and lesser green s function matrices which extend formulas derived by takahashi and others we show that these recurrences may lead to a dramatically reduced computational cost because they only require computing a small number of entries of the inverse matrix then we propose a parallelization strategy for block tridiagonal matrices which involves a combination of schur complement calculations and cyclic reduction it achieves good scalability even on problems of modest size

margin error bounds for support vector machines on reproducing kernel banach spaces support vector machines which maximize the margin from patterns to the separation hyperplane subject to correct classification have received remarkable success in machine learning margin error bounds based on hilbert spaces have been introduced in the literature to justify the strategy of maximizing the margin in svm recently there has been much interest in developing banach space methods for machine learning large margin classification in banach spaces is a focus of such attempts in this letter we establish a margin error bound for the svm on reproducing kernel banach spaces thus supplying statistical justification for large margin classification in banach spaces

characteristic inequalities of uniformly convex and uniformly smooth banach spaces abstract let x be a real banach space with dual x and moduli of convexity and smoothness x e and x respectively for 1 p denotes the duality mapping from x into 2 x with gauge function t p 1 and j p denotes an arbitrary selection for j p let a r 0 0 t is strictly increasing and there exists c 0 such that t c x t 2 and f r 0 0 t is convex nondecreasing and there exists k 0 such that k x it is proved that x is uniformly convex if and only if there is a a such that x y p x p p j p x y x y x y x and x is uniformly smooth if and only if there is a f such that x y p x p p j p x y x y x y x where for given function f f x y is defined by f x y p 0 1 x ty x p t f t y x ty x dt these inequalities which have various applications can be regarded as general banach space versions of the well known polarization identity occurring in hilbert spaces

resolvent operator technique for generalized implicit variational like inclusion in banach space a new class of g accretive mappings is introduced and studied in banach space by using the properties of g accretive mappings the concept of resolvent operators associated with the classical m accretive operators is extended and an iterative algorithm for a new class of generalized implicit variational like inclusion involving g accretive mappings and its convergence results are established in banach space

a necessary and sufficient condition for convergence of steepest descent approximation to accretive operator equations abstract a necessary and sufficient condition is established which ensures the strong convergence of the steepest descent approximation to a solution of equations involving quasi accretive operators defined on a uniformly smooth banach space

a three dimensional explicit preconditioned solver a new class of generalized approximate inverse matrix gaim techniques based on the concept of lu sparse factorization procedures is introduced for computing explicitly generalized approximate inverses of large sparse unsymmetric matrices of regular structure without inverting the decomposition factors explicit preconditioned iterative methods in conjunction with modified forms of the gaim techniques are presented for solving numerically boundary value problems in three dimensions the numerical implementation of these algorithms is presented and fortran subroutines are given

demiclosedness principle and convergence theorems for k strictly asymptotically pseudocontractive maps let e be a real q uniformly smooth banach space which is also uniformly convex for example lp or lp spaces 1 p and k a nonempty closed convex not necessarily bounded subset of e let t k k be a k strictly asymptotically pseudocontractive map with a nonempty fixed point set it is proved that i t is demiclosed at 0 furthermore weak and strong convergence of an averaging iteration method to a fixed point of t are proved

strong convergence theorems for maximal monotone mappings in banach spaces let e be a uniformly convex and 2 uniformly smooth real banach space with dual e let a e e be a lipschitz continuous monotone mapping with a 1 0 for given u x1 e let xn be generated by the algorithm xn 1 nu 1 n xn najxn n 1 where j is the normalized duality mapping from e into e and n and n are real sequences in 0 1 satisfying certain conditions then it is proved that under some mild conditions xn converges strongly to x e where jx a 1 0 finally we apply our convergence theorems to the convex minimization problems

properties of min max controllers in uncertain dynamical systems we discuss properties of min max controllers previously obtained for uncertain dynamical systems in particular we present a new model for switching action and re examine asymptotic stability we demonstrate the attractiveness of switching surfaces and comment on the insensitivity of solutions in those surfaces to the uncertainty

the iterative solution of the equation f x tx for a monotone operator t in lp spaces suppose t is a multivalued monotone operator not necessarily continuous with open domain d t in lp 2 p f r i t and the equation f x tx has a solution q d t then there exists a neighbourhood b d t of q and a real number r1 0 such that for any r r1 for any initial guess x1 b and any singlevalued section t0 of t the sequence xn n 1 generated from x1 by xn 1 1 cn xn cn f t0xn remains in d t and converges strongly to q with xn q 0 n 1 2 furthermore for x lp e e

steepest descent approximations for accretive operator equations a necessary and sufficient condition is established for the strong convergence of the steepest descent approximation to a solution of equations involving quasi accretive operators defined on a uniformly smooth banach space miramare trieste march 1993

ball algorithms for constructing solutions of nonlinear operator equations abstract in the most general setting we extend the previous theory of the region contraction algorithm developed recently by several authors for solving nonlinear operator equations it is demonstrated that the extended algorithm still possesses properties such as generating error bounds automatically providing a computational test for the existence of solutions and being globally convergent under nominal conditions as example of applications we specialize the extended theory in particular to nonlinear operator equations of monotone type

convergence rates for inverse problems with impulsive noise we study inverse problems f f g with perturbed right hand side g rm obs corrupted by so called impulsive noise i e noise which is concentrated on a small subset of the domain of definition of g it is well known that tikhonov type regularization with an mathbf l 1 data fidelity term yields significantly more accurate results than tikhonov regularization with classical mathbf l 2 data fidelity terms for this type of noise the purpose of this paper is to provide a convergence analysis explaining this remarkable difference in accuracy our error estimates significantly improve previous error estimates for tikhonov regularization with mathbf l 1 fidelity term in the case of impulsive noise we present numerical results which are in good agreement with the predictions of our analysis

automatic tuning of decentralized pid controllers for tito processes this paper presents a new algorithm for automatic tuning of decentralized pid control for two input two output tito plants that fully extends the single loop relay auto tuner to the multiloop case the tuning procedure consists of two stages in the first the desired critical point which consists of the critical gains of the two loops and a critical frequency is identified unlike siso plants there are infinitely many such points and knowledge of the desired one is essential to the tuning procedure the auto tuner identifies the desired critical point with almost no a priori information on the process during the identification phase all controllers are replaced by relays thus generating limit cycles with the same period in both loops it is shown that each limit cycle corresponds to a single critical point of the process by varying the relay parameters different critical points can be determined the auto tuner contains a procedure that converges rapidly to the desired critical point while maintaining the amplitudes of the process variables as well as of the manipulated variables within prespecified ranges in the second stage the data of the desired critical point and possibly of other critical points is used to tune the pid controller by the ziegler nichols rule or its modifications this paper focuses on the first stage the steady state process gains which are required for the appropriate choice of the desired critical point are determined by the auto tuner in closed loop fashion simultaneously with the identification of the critical points the identification of the process gains is achieved at no extra plant time on the basis of a large number of simulated cases the proposed auto tuner seems to be efficient and robust this paper discusses the underlying principles of the auto tuner and its properties and capabilities demonstrated via examples the algorithm is not limited to tito cases and can be extended to any number of loops

coincidence points by generalized mann iterates with applications in hilbert spaces this paper deals with the construction of the coincidence points by the generalized mann iterates and their applications in hilbert spaces our results generalize and improve a number of recent results

approximation of common fixed points for finite families of total asymptotically nonexpansive mappings abstract let e be a real banach space k a closed convex nonempty subset of e let t 1 t 2 t m k k be m total asymptotically nonexpansive mappings an iterative sequence for approximation of common fixed points assuming existence of t 1 t 2 t m is constructed necessary and sufficient conditions for the convergence of the scheme to a common fixed point of the mappings are given furthermore in the case that e is uniformly convex a sufficient condition for convergence of the iteration process to a common fixed point of mappings under our setting is established

second order sufficient conditions for error bounds in banach spaces recently huang and ng presented second order sufficient conditions for error bounds of continuous and ga teaux differentiable functions in banach spaces wu and ye dropped the assumption of huang and ng on ga teaux differentiability but required the space to be a hilbert space we carry on this research in two directions first we extend wu and ye s result to some non hilbert spaces second same as huang and ng we work on banach spaces but provide different second order sufficient conditions that may allow the function to be non ga teaux differentiable

higher order convergence rates for bregman iterated variational regularization of inverse problems we study the convergence of variationally regularized solutions to linear ill posed operator equations in banach spaces as the noise in the right hand side tends to 0 the rate of this convergence is determined by abstract smoothness conditions on the solution called source conditions for non quadratic data fidelity or penalty terms such source conditions are often formulated in the form of variational inequalities such variational source conditions vscs as well as other formulations of such conditions in banach spaces have the disadvantage of yielding only low order convergence rates a first step towards higher order vscs has been taken by grasmair j inverse ill posed probl 21 3 379 394 2013 https doi org 10 1515 jip 2013 0002 who obtained convergence rates up to the saturation of tikhonov regularization for even higher order convergence rates iterated versions of variational regularization have to be considered in this paper we introduce vscs of arbitrarily high order which lead to optimal convergence rates in hilbert spaces for bregman iterated variational regularization in banach spaces with general data fidelity and penalty terms we derive convergence rates under third order vsc these results are further discussed for entropy regularization with elliptic pseudodifferential operators where the vscs are interpreted in terms of besov spaces and the optimality of the rates can be demonstrated our theoretical results are confirmed in numerical experiments

on computing the inverse of a sparse matrix the gauss jordan inversion algorithm requires 0 n3 arithmetic operations in some practical applications like state estimation or short circuit calculation in power systems the given matrix is sparse and only part of the inverse is needed most frequently in the diagonal dominant case this is the diagonal there are two ways to exploit sparsity to determine elements of the inverse 1columnwise inversion via the solution of sparse linear systems with columns of the unit matrix as right hand sides 2application of the algorithm of takahashi et al6 the latter algorithm arises very naturally from multiplying the left and right hand factors of the zollenkopf bifactorization in reverse order we indicate how computing time can be gained in the important symmetric diagonal dominant case if only part of the diagonal is needed and compare computing times of the method of takahasi et al 6 with several variants of columnwise inversion whereas most of the theory holds for general matrices experiments are performed on the symmetric diagonal dominant case for band matrices the operation count is 0 n both for computing a column of the inverse by columnwise inversion and the diagonal by the algorithm of takahashi et al6

inequalities in banach spaces with applications well known that many problems in a hilbert space h are solved by applying the following identity ilax 1 a yi12 a412 1 llyl12 a 1 mx yl12 1 1 for all x y in h and 0 5 i 5 1 therefore one natural method to solve problems in a banach space xis to establish equalities and usually inequalities in xanalogous to 1 1 this is in fact shown by some authors recent work see for example reich l poffald and reich 2 lim 3 lim et af 4 prus and smarzewski 5 smarzewski 6 and reich 21 the purpose of this paper is to continue carrying out investigations in this line more precisely in section 3 we establish some inequalities analogous to 1 l in either uniformly convex or uniformly smooth banach spaces as corollaries we obtain new characteristics of p uniform convexity and q uniform smoothness of a banach space x via the functionals i lip and ii llq respectively we give in section 4 applications of the inequalities obtained in section 3 to fixed points of uniformly lipschitzian mappings and to best approximation theory

characteristic conditions for convergence of generalized steepest descent approximation to multivalued accretive operator equations abstract in the present paper sufficient and necessary conditions for convergence of generalized steepest descent approximation to multivalued accretive operator equations are established for the sufficiency part and a specific error estimation is also given

on the rate of convergence of iterated bregman projections and of the alternating algorithm abstract we study the alternating algorithm for the computation of the metric projection onto the closed sum of two closed subspaces in uniformly convex and uniformly smooth banach spaces for banach spaces which are convex and smooth of power type we exhibit a condition which implies linear convergence of this method we show these convergence results for iterates of bregman projections onto closed linear subspaces using an intimate connection between the metric projection onto a closed linear subspace and the bregman projection onto its annihilator we deduce the convergence rate results for the alternating algorithm from the corresponding results for the iterated bregman projection method

iterative approximations of fixed points and solutions for strongly accretive and strongly pseudo contractive mappings in banach spaces abstract in this article we prove some new convergence theorems of the ishikawa and mann iteration sequences for strongly accretive and strongly pseudo contractive mappings by using the new inequality and the new approximation methods our main results improve and extend the corresponding results of j math anal appl 151 1990 453 461 proc amer math soc 120 1994 545 551 j math appl 192 1995 502 518 j math anal appl 174 1993 441 449 acta appl math 32 1993 183 196 nonlinear anal tma 24 1995 981 987 j math anal appl 178 1993 9 21 proc amer math soc 125 6 1997 1705 1709

generalized mann iterates for constructing fixed points in hilbert spaces the mean iteration scheme originally proposed by mann is extended to a broad class of relaxed inexact fixed point algorithms in hilbert spaces weak and strong convergence results are established under general conditions on the underlying averaging process and the type of operators involved this analysis significantly widens the range of applications of mean iteration methods several examples are given

asymptotic behavior of the solutions of non autonomous systems in banach spaces abstract in this paper we study the weak and strong convergence of the integral solution of the following nonlinear evolution inclusion u t a t u t f t t 0 u 0 x 0 where a t t 0 is a family of m accretive operators and f is a multi function which extends some results in this area