vector valued variational principle in fuzzy metric space and its applications a vector valued ekeland s variational principle and its equivalents in fuzzy metric space are presented in this paper our result unifies and extends some of the previous results about single valued and vector valued ekeland s variational principle as an application we obtain a fixed point theorem in fuzzy metric space under a new contractive condition which is a new generalization of well known banach contraction principle all of our results are also new even in usual metric spaces

line search acceleration of iterative methods abstract this paper describes and analyzes a simple technique that accelerates the convergence of iterative methods for solving large linear systems the proposed technique can be used with any convergent method however it is especially useful when solving unstructured systems since in this case traditional methods as sor or chebyshev semiiteration have difficulty in obtaining optimal parameters special attention is given to column relaxation and row relaxation it is demonstrated experimentally that an accelerated gauss seidel scheme runs faster than an optimally tuned sor scheme

solving linear systems involved in constrained optimization abstract many interior point methods for large scale linear programming quadratic programming the convex programming solve an n m n m linear system in each iteration the last m equations require exact solutions in order to maintain the feasibility current implementations reduce that step to solving an m m linear system the solution must be exact because otherwise the error would be entirely passed on to the last m equations of the original system this makes the computation costly and sometimes impractical in this paper we propose an inexpensive iterative method for solving that n m n m system it guarantees exact solutions to the last m equations the convergence is proved and the implementational issues are discussed some preliminary numerical results are also reported

fixed point theorems for nonlinear contractions in kaleva seikkala s type fuzzy metric spaces in this paper the existence and unicity of fixed points for mappings in fuzzy metric spaces in the sense of kaleva and seikkala is discussed nonlinear contractions of the boyd wong s type alber guerre delabriere s type and kannan reich s type are considered and several new fixed point theorems for these contractions in complete fuzzy metric spaces are presented respectively also some error estimates are given for iterations to approximate fixed point previous work with respect to fixed point in fuzzy metric spaces is based on the t conorm max the presented work does away with this restriction by proposing weaker conditions defining a generic class of suitable binary operations as applications the corresponding fixed point theorems for menger probabilistic metric spaces are obtained

on the triangle inequalities in fuzzy metric spaces this paper presents level forms of the triangle inequalities in fuzzy metric spaces x d l r to aid discussion a fuzzy pre metric condition is introduced it is first pointed out that under the fuzzy pre metric condition the first triangle inequality is always equivalent to its level form the second triangle inequality is equivalent to one level form when r is right continuous and to another level form also when further conditions are imposed on r in a fuzzy metric space the level form of the first triangle inequality and one of the level forms of the second triangle inequality are always valid the other level form of the second triangle inequality holds for all but at most countable a 0 1 finally a fixed point theorem for fuzzy metric spaces is derived as an application of the preceding results

iterative solution of linear systems in the 20th century this paper sketches the main research developments in the area of iterative methods for solving linear systems during the 20th century although iterative methods for solving linear systems nd their origin in the early 19th century work by gauss the eld has seen an explosion of activity spurred by demand due to extraordinary technological advances in engineering and sciences the past ve decades have been particularly rich in new developments ending with the availability of large toolbox of specialized algorithms for solving the very large problems which arise in scientic and industrial computational models as in any other scientic area research in iterative methods has been a journey characterized by a chain of contributions building on each other it is the aim of this paper not only to sketch the most signicant of these contributions during the past century but also to relate them to one another c 2000 elsevier science b v all rights reserved

perturbation analysis for the projection of a point to an affine set abstract we present a perturbation analysis for the projection of a point to an affine set in r n the matrix involved is not assumed to be full rank and the perturbation is arbitrary error bounds for the solution under the rank preserving and rank nondecreasing perturbations are obtained the results given here appear to be the most general up to now

a projection method for semidefinite linear systems and its applications we study the solution of consistent semidefinite and symmetric linear systems by iterative techniques given a finite sequence of subspaces a block iterative projection type algorithm is considered for two specific choices of iteration parameters we show convergence we apply our results to over and under determined linear equations these methods are based on decomposing the system matrix into blocks of rows or blocks of columns thereby several algorithms many used in image reconstruction are presented in a unified way

an extension of ekeland s variational principle in fuzzy metric space and its applications abstract an extension of ekeland s variational principle in fuzzy metric space which is an essential and the most general improvement of ekeland s variational principle in fuzzy metric space up to now is established as an application we obtain caristi s coincidence theorem for set valued mappings in fuzzy metric spaces further a direct simple proof of the equivalence between the two theorems is given some applications of these results to probabilistic metric spaces are presented all these results even in usual metric space are also the latest

a new class of preconditioners for large scale linear systems from interior point methods for linear programming a new class of preconditioners for the iterative solution of the linear systems arising from interior point methods is proposed for many of these methods the linear systems are symmetric and indefinite the system can be reduced to a system of normal equations which is positive definite we show that all preconditioners for the normal equations system have an equivalent for the augmented system while the opposite is not true the new class of preconditioners works better near a solution of the linear programming problem when the matrices are highly ill conditioned the preconditioned system can be reduced to a positive definite one the techniques developed for a competitive implementation are rather sophisticated since the subset of columns is not known a priori the new preconditioner applied to the conjugate gradient method compares favorably with the cholesky factorization approach on large scale problems whose cholesky factorization contains too many nonzero entries

nonconvex fuzzy mappings and the fuzzy pre variational inequality in this paper we introduce the concepts of fuzzy pseudoconvex fuzzy invex fuzzy pseudoinvex and fuzzy preinvex mapping from r n to the set of fuzzy numbers and put forward the concepts of fuzzy extended directional differential subgradient and subdifferential some properties are obtained for fuzzy pseudoconvex fuzzy invex fuzzy pseudoinvex and fuzzy preinvex mapping relations are discussed between the fuzzy pre variational inequality and the fuzzy vector optimization problem

beams on a two dimensional pasternak base subjected to loads that cause lift off abstract first two closely related problems shown in fig 1 published by chernigovskaya 1961 in issledovaniya po dinamike sooruzhenii i raschetu konstruktsii na uprugoni osnovanii edited by b g korenev pp 113 141 gosstroiizdat moscow and ting 1973 j franklin inst 296 2 77 89 are discussed it is shown that neither of their formulations is correct the aim of this paper is to show how to correctly formulate and solve problems of this type utilizing the variational approach for variable matching points derived by kerr 1976 int j solids structures 12 1 11 a formulation lor the problem analyzed by ting is presented that is mechanically reasonable and mathematically well posed the analytical solution obtained is evaluated numerically and then compared with related test results by durelli et al 1969 j struct div asce 95 1713 1725 this paper concludes with a discussion of the results obtained

a sparse approximate inverse preconditioner for the conjugate gradient method a method for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix a is developed and the resulting factorized sparse approximate inverse is used as an explicit preconditioner for conjugate gradient calculations it is proved that in exact arithmetic the preconditioner is well defined if a is an h matrix the results of numerical experiments are presented

on fuzzy metric spaces abstract in this paper we introduce the concept of a fuzzy metric space the distance between two points in a fuzzy metric space is a non negative upper semicontinuous normal and convex fuzzy number properties of fuzzy metric spaces are studied and some fixed point theorems are proved

a direct projection method for sparse linear systems an oblique projection method is adapted to solve large sparse unstructured systems of linear equations this row projection technique is a direct method which can be interpreted as an oblique kaczmarz type algorithm and is also related to other standard solution methods when a sparsity preserving pivoting strategy is incorporated it is demonstrated that the technique can be superior in terms of both fill in and arithmetic complexity to more standard sparse algorithms based on gaussian elimination this is especially true for systems arising from stiff ordinary differential equations problems in chemical kinetics studies

generalized convex fuzzy mappings and fuzzy variational like inequality in this paper we introduce the concepts of some generalized convex fuzzy mappings from r n to the set of fuzzy numbers under the condition of upper or lower semicontinuity a new criterion be obtained for the existence of a fuzzy preinvex mapping a fuzzy preinvex mapping can be achieved when the invex subset of r n satisfies certain conditions the relations between generalized convex fuzzy mappings are discussed and some properties are obtained that relate the concepts of fuzzy pseudoinvex and fuzzy prequasiinvex mapping fuzzy invex and fuzzy preinvex mapping fuzzy preinvex and fuzzy prequasiinvex mapping we also discuss the relationship between the fuzzy variational like inequality the fuzzy weak variational like inequality and fuzzy optimization problems and an application example of a fuzzy variational like inequality the fuzzy variational like inequality representation of a fuzzy transportation equilibrium problem

minimization theorems for fixed point theorems in fuzzy metric spaces and applications abstract in this paper we establish a minimization theorem in fuzzy metric spaces and make use of the result to obtain a fixed point theorem in fuzzy metric spaces which is similar to the downing kirk fixed point theorem in metric spaces as the consequences we obtain caristi s fixed point theorem and ekeland s variational principle in fuzzy metric spaces and also give a direct simple proof of the equivalence between these two theorems some applications of these results to probabilistic metric spaces are presented

a generalized model of elastic foundation based on long range interactions integral and fractional model abstract the common models of elastic foundations are provided by supposing that they are composed by elastic columns with some interactions between them such as contact forces that yield a differential equation involving gradients of the displacement field in this paper a new model of elastic foundation is proposed introducing into the constitutive equation of the foundation body forces depending on the relative vertical displacements and on a distance decaying function ruling the amount of interactions different choices of the distance decaying function correspond to different kind of interactions and foundation behavior the use of an exponential distance decaying function yields an integro differential model while a fractional power law decay of the distance decaying function yields a fractional model of elastic foundation ruled by a fractional differential equation it is shown that in the case of exponential decaying function the integral equation represents a model in which all the gradients of the displacement function appear while the fractional model is an intermediate model between integral and gradient approaches a fully equivalent discrete point spring model of long range interactions that may be used for the numerical solution of both integral and fractional differential equation is also introduced some green s functions of the proposed model have been included in the paper and several numerical results have been also reported to highlight the effects of long range forces and the governing parameters of the linear elastic foundation proposed

on the error estimate for the projection of a point onto a linear manifold abstract suppose that the linear system a h x b is consistent the problem of finding the solution x to min a h x b 1 2 x p 2 2 is studied where a c n m b c m x p c n and a b p are given when a b and p are perturbed an error bound for the solution x is obtained roundoff error bounds for the singular value decomposition method the column pivoting method and the rank revealing method are obtained the results in this paper extend those of arioli laratta and menchi to the case when a is not of full rank and either m n or m n

on the level convergence of a sequence of fuzzy numbers abstract in this paper we first give a simplified proof of the existence theorem of supremum and infimum in fuzzy number space e 1 established by wu and wu j math anal appl 210 1997 499 and improve the expressions of the supremum and infimum as a straightforward corollary of this result we obtain a necessary and sufficient condition under which for a bounded sequence of fuzzy numbers u n the pair of functions sup n u n and sup n u n can determine a fuzzy number secondly we give a necessary and sufficient condition for a sequence of fuzzy numbers u n to be levelwise convergent in e 1 and generalize some important theorems in real number spaces to fuzzy number spaces finally we prove the existence of supremum and infimum for the level continuous fuzzy valued function on a closed interval and give a necessary and sufficient condition under which its supremum and infimum can be attained

set valued ekeland variational principles in fuzzy metric spaces abstract in this paper we establish a general set valued ekeland s variational principle in fuzzy metric spaces where the objective function is a set valued map defined on a fuzzy metric space and taking values in a pre ordered locally convex space and the perturbation involves a quasi metric family generating the fuzzy topology of the domain space moreover the direction of the perturbation is a convex subset of the positive cone instead of a single positive vector in our general version the assumption that the objective function is lower semi continuous and one that the range of the function is lower bounded are both weakened from the general ekeland s variational principle we obtain several particular set valued ekeland s variational principles in fuzzy metric spaces which generalize and improve some related known results from these we deduce the corresponding caristi s fixed point theorems for set valued maps and the corresponding takahashi s non convex minimization theorems in set valued optimization finally we extend the obtained results to f type topological spaces

the variational principle in fuzzy metric spaces and its applications abstract in this paper we prove a fixed point theorem and a variational principle in fuzzy metric spaces applying these results to some probabilistic metric spaces we obtain a corresponding fixed point theorem and a variational principle

coincidence theorems for set valued mappings and ekeland s variational principle in fuzzy metric spaces abstract in this paper we establish a coincidence theorem for set valued mappings in fuzzy metric spaces with a view to generalizing downing kirk s fixed point theorem in metric spaces as consequences we obtain caristi s coincidence theorem for set valued mappings and a more general type of ekeland s variational principle in fuzzy metric spaces further we also give a direct simple proof of the equivalence between these two theorems in fuzzy metric spaces some applications of these results to probabilistic metric spaces are presented

error analysis of algorithms for computing the projection of a point onto a linear manifold the accumulation of rounding errors in methods used to compute the projection of a point onto a linear manifold is studied the methods are based on modified gram schmidt householder and givens orthogonal factorizations

iterative refinement of solution with biparameter for solving ill conditioned systems of linear algebraic equations although the idea of iteration refinement for improving the computed solution to a system of linear equations can go back to 1948 the technique has remained popular siam philadelphia pa 1998 bit 17 1977 303 math comput 35 1980 817 j numer anal 17 4 1997 495 in this paper a new iterative improvement of solution with biparameter for solving ill conditioned systems of linear algebraic equations is proposed both theoretical convergence analysis and numerical experiments are presented to show the efficiency and accuracy of our method

finding the orthogonal projection of a point onto an affine subspace a simple method is proposed to find the orthogonal projection of a given point to the solution set of a system of linear equations this is also a direct method for solving systems of linear equations the output of the method is either the projection or inconsistency of the system moreover in the process also linearly dependent equations are recognized this paper is constrained for giving theoretical foundations computational complexity and some numerical experiments with dense matrices although the method allows to employ sparsity the raw method could not compete with best software packages in solving linear equations for general matrices but it was competitive in finding projections for matrices with small number of rows relative to the number of columns

set valued pseudo metric families and ekeland s variational principles in fuzzy metric spaces abstract in this paper we introduce a set valued pseudo metric family on a fuzzy metric space and the notion of compatibility between the set valued pseudo metric family and the original fuzzy metric by means of this notion we prove a general set valued evp where the perturbation involves a set valued pseudo metric family compatible with the original fuzzy metric from the general evp we deduce several particular evps which extend the evps in qiu 2013 36 and in gutierrez et al 2008 20 to fuzzy metric spaces by using set valued pseudo metric families and using the unified approach for approximate solutions introduced by gutierrez jimenez and novo we deduce a general version of set valued evp based on c efficient solutions in fuzzy metric spaces where c is a coradiant set contained in the order cone by choosing two specific versions of the coradiant set c in the general version of evp we obtain several particular set valued evps for efficient solutions in the sense of nemeth and of dentcheva and helbig respectively these evps improve and generalize the related known results

axisymmetric forced vibrations of an elastic free circular plate on a tensionless two parameter foundation the static and dynamic responses of a circular elastic plate on a two parameter tensionless foundation are investigated by assuming that the external load is rotationally symmetric and the plate experiences axially symmetric displacements in the solution procedure the vertical displacement of the foundation is determined by the corresponding governing equation whereas the vertical displacement of the plate is expressed in series in terms of the mode shapes of the completely free circular plate for the case of complete contact the corresponding governing equation of the plate incorporated with the edge reaction from the foundation is satisfied through the galerkin s approximation technique the contact radius is obtained by requiring that the surface of the foundation satisfies the corresponding continuity equations it is shown that the problem displays a highly nonlinear character due to the lift off of the plate from the foundation and the numerical treatment of the governing equation is accomplished by adopting iterative processes in terms of the contact radius the governing equation of the problem is solved numerically for the static and dynamic cases and the results are presented in figures to demonstrate the nonlinear behavior of the plate for various values of the parameters of the problem comparatively