lower bounds for the perron root of a nonnegative matrix abstract new lower bounds frequently better than previous bounds and readily computable for the perron root r a of a nonnegative matrix a are obtained the theoretical comparison of new bounds with the known ones is supplemented with two numerical examples

random fixed points of random multivalued operators on polish spaces random coincidence point theorems and random fixed point theorems are stochastic generalizations of classical coincidence point theorems and classical fixed point theorems random fixed point theorems for contraction mappings in polish spaces were proved by spacek l and hans 2 31 for a complete survey we refer to bharucha reid 4 itoh 5 proved several random fixed point theorems and gave their applications to random differential equations in banach spaces recently sehgal and singh 7 papageorgiou 8 and lin 9 have proved different stochastic versions of the well known schauder s fixed point theorem the aim of this paper is to prove various stochastic versions of banach type fixed point theorems for multivalued operators section 2 is aimed at clarifying the terminology to be used and recalling basic definitions and facts section 3 deals with random coincidence point theorems for a pair of compatible random multivalued operators the structure of common random fixed points of these operators is also studied in section 4 the existence of a common random fixed point of two random multivalued operators satisfying the meir keeler type condition in polish spaces is proved section 5 contains a random fixed point theorem for a pair of locally contractive random multivalued operators in s chainable polish spaces as an application a theorem on random approximation is also obtained

some lower bounds for the spectral radius of matrices using traces abstract let a be an n n matrix with eigenvalues 1 2 n and let m be an integer satisfying rank a m n if a is real the best possible lower bound for its spectral radius in terms of m tr a and tr a 2 is obtained if a is any complex matrix two lower bounds for j 1 n j 2 are compared and furthermore a new lower bound for the spectral radius is given only in terms of tr a tr a 2 a a a aa n and m

a sequence of lower bounds for the spectral radius of nonnegatfve matrices abstract we present a sequence of progressively better lower bounds for the s pectral radius of a nonnegative matrix each element of the sequence is a function of the spectral radius of the geometric symmetrization of a power of the matrix as defined by schwenk each element provides a better approximation to the spectral radius than the elements in the sequences provided by other authors

an existence theorem for quasiconcave functions with applications on demontre un theoreme d existence pour certaines familles de fonctions quasi concaves sur un ensemble compact convexe et on donne des applications de ce theoreme aux espaces localement convexes normes de hilbert et de dimension finie

spatial activity allocation modelling the dominant eigenvalue and its corresponding eigenvector for the garin lowry model criteria are derived for convergence and it is shown how the forecasts are affected by changes in the parameters of the model and by fluctuations in the exogenous variables convergence occurs if and only if the dominant eigenvalue is smaller than one expressing the upper and lower bounds for the dominant eigenvalue in terms of the parameters of the model yields interpretable convergence conditions for the sensitivity analysis the model is rewritten as an eigensystem in which the endogenous variables appear as the elements of the eigenvector corresponding with the dominant eigenvalue that is the perron vector the sensitivity of the forecasts is analyzed by examining the effects of perturbations in a matrix on the perron vector

lower bounds for the spectral radius of a matrix abstract we develop lower bounds for the spectral radius of symmetric skew symmetric and arbitrary real matrices our approach utilizes the well known leverrier faddeev algorithm for calculating the coefficients of the characteristic polynomial of a matrix in conjunction with a theorem by lucas which states that the critical points of a polynomial lie within the convex hull of its roots our results generalize and simplify a proof recently published by tarazaga for a lower bound on the spectral radius of a symmetric positive definite matrix in addition we provide new lower bounds for the spectral radius of skew symmetric matrices we apply these results to a problem involving the stability of fixed points in recurrent neural networks

bounds on the joint and generalized spectral radius of the hadamard geometric mean of bounded sets of positive kernel operators abstract let 1 m be bounded sets of positive kernel operators on a banach function space l we prove that for the generalized spectral radius and the joint spectral radius the inequalities 1 1 m m 1 m 1 2 m 1 m 1 1 m m 1 m 1 2 m 1 m hold where 1 1 m m 1 m denotes the hadamard schur geometric mean of the sets 1 m

sharp bounds for the largest eigenvalue of the signless laplacian of a graph let g be a simple connected graph with n vertices and m edges denote the degree of vertex vi by d vi the matrix q g d g a g is called the signless laplacian of g where d g diag d v1 d v2 d vn and a g denote the diagonal matrix of vertex degrees and the adjacency matrix of g respectively let q1 g be the largest eigenvalue of q g in this paper we first present two sharp upper bounds for q1 g involving the maximum degree and the minimum degree of the vertices of g and give a new proving method on another sharp upper bound for q1 g then we present three sharp lower bounds for q1 g involving the maximum degree and the minimum degree of the vertices of g moreover we determine all extremal graphs which attain these sharp bounds

a sequence of upper bounds for the perron root of a nonnegative matrix abstract we present a sequence of progressively better upper bounds for the perron root of a nonnegative matrix each element in the sequence is a function of the perron root of the arithmetic symmetrization of a power of the matrix the results complement those of szyld based on the geometric symmetrization of a power of the matrix

on matrices whose numerical ranges have circular or weak circular symmetry in 18 among other equivalent conditions it is proved that a square complex matrix a is permutationally similar to a block shift matrix if and only if for any complex matrix b with the same zero pattern as a w b the numerical range of b is a circular disk centered at the origin in this paper we add a long list of further new equivalent conditions the corresponding result for the numerical range of a square complex matrix to be invariant under a rotation about the origin through an angle of 2 m where m 2 is a given positive integer is also proved many interesting by products are obtained in particular on the numerical range of a square nonnegative matrix a the following unexpected results are established i when the undirected graph of a is connected if w a is a circular disk centered at the origin then so is w b for any complex matrix b with the same zero pattern as a ii when a is irreducible if is an eigenvalue in the peripheral spectrum of a that lies on the boundary of w a then is a sharp point of w a we also obtain results on the numerical range of an irreducible square nonnegative matrix which strengthen or clarify the work of issos 9 and nylen and tam 14 on this topic open questions are posed at the end

nested bounds for the perron root of a nonnegative matrix abstract it is well known that for a nonnegative matrix a the smallest row sum r a and the largest row sum r a provide lower and upper bounds respectively for the perron root of a these bounds are generalized for a partitioned nonnegative matrix a the new bounds are better than r a and r a and they can be further improved by a refinement of the partition known monotonicity and convergence properties of r a and r a are generalized for the new bounds

numerical ranges of companion matrices we show that an n by n companion matrix a can have at most n line segments on the boundary w a of its numerical range w a and it has exactly n line segments on w a if and only if for n odd a is unitary and for n even a is unitarily equivalent to the direct sum a1 a2 of two n 2 by n 2 companion matrices a1

on the symmetric form of systems of conservation laws with entropy abstract this paper reviews the symmetrizability of systems of conservation laws which possess entropy functions symmetric formulations in conservation form for the equations of gas dynamics are presented

the numerical range of a nonnegative matrix abstract we offer an almost self contained development of perron frobenius type results for the numerical range of an irreducible nonnegative matrix rederiving and completing the previous work of issos nylen and tam and tam and yang on this topic we solve the open problem of characterizing nonnegative matrices whose numerical ranges are regular convex polygons with center at the origin some related results are obtained and some open problems are also posed

on the knaster kuratowski mazurkiewicz shapley theorem 1 it is well known that the celebrated k k m theorem knaster et al 4 on closed coverings of a simplex is equivalent to brouwer s fixed point theorem recently shapley 8 used the pathfollwing technique of lemke and howson 5 and scarf 6 7 to establish a generalization of the k k m theorem the generalized result is here called the k k m s theorem which is interesting in its own right the purpose of the present note is to show that the k k m s theorem is a simple consequence of a theorem of ky fan on a generalization of kakutani s fixed point theorem the present author would like to acknowledge that the essential idea of this note is borrowed from kannai 3

entropy flux splittings for hyperbolic conservation laws part i general framework a general framework is proposed for the derivation and analysis of flux splittings and the corresponding flux splitting schemes for systems of conservation laws endowed with a strictly convex entropy the approach leads to several new properties of the existing flux splittings and to a method for the construction of entropy flux splittings for general situations a large family of genuine entropy flux splittings is derived for several significant examples the scalar conservation laws the p system and the euler system of isentropic gas dynamics in particular for the isentropic euler system we obtain a family of splittings that satisfy the entropy inequality associated with the mechanical energy for this system it is proved that there exists a unique genuine entropy flux splitting that satisfies all of the entropy inequalities which is also the unique diagonalizable splitting this splitting can be also derived by the so called kinetic formulation simple and useful difference schemes are derived from the flux splittings for hyperbolic systems such entropy flux splitting schemes are shown to satisfy a discrete cell entropy inequality for the diagonalizable splitting schemes an a priori l estimate is provided by applying the principle of bounded invariant regions the convergence of entropy flux splitting schemes is proved for the 2 2 systems of conservation laws and the isentropic euler system 1995 john wiley sons inc

construction of bgk models with a family of kinetic entropies for a given system of conservation laws we introduce a general framework for kinetic bgk models we assume to be given a system of hyperbolic conservation laws with a family of lax entropies and we characterize the bgk models that lead to this system in the hydrodynamic limit and that are compatible with the whole family of entropies this is obtained by a new characterization of maxwellians as entropy minimizers that can take into account the simultaneous minimization problems corresponding to the family of entropies we deduce a general procedure to construct such bgk models and we show how classical examples enter the framework we apply our theory to isentropic gas dynamics and full gas dynamics and in both cases we obtain new bgk models satisfying all entropy inequalities

hyperbolic forms associated with cyclic weighted shift matrices abstract the singular points of the curve of a hyperbolic form associated with a cyclic weighted shift matrix are examined it is shown that the singular points of such a curve are real nodes some results related the numerical ranges of cyclic weighted shift matrices are presented in particular the existence of flat portions on the boundary of the numerical range depends on the reducibility of the hyperbolic form further an algebraic method is provided for the decomposition of reducible form which leads to a criterion for the periodicity of the weights

the boundary of higher rank numerical ranges abstract the rank k numerical range of an n n matrix a is defined as k a c pap p for some rank k orthogonal projection p this study presents a method to generate the boundary of k a and examines the flat portions of the boundary of the rank k numerical range of a matrix associated with a roulette curve a sufficient condition is given to ensure that the rank k numerical range is not attainable by a classical numerical range

derivatives of the perron root at an essentially nonnegative matrix and the group inverse of an m matrix abstract the results of the work in this paper can be divided into two major parts in the first part we develop formulae using group inverses of irreducible m matrices for the second order partial derivatives with respect to the entries of the perron root r at an essentially nonnegative and irreducible matrix a we use these formulae to obtain explicit expressions for the matrices 2 r a ij 2 and 2 r a ii jj and examine these expressions at some special cases when for example in addition to a being essentially nonnegative and irreducible a is row stochastic or a is of rank 1 and so on in the second major part of this paper we investigate for a singular and irreducible m matrix q a certain matrix g which is a positive diagonal scaling of the group inverse q of q we show for instance that z gz 0 for all real vectors z and use this result and some of the formulae obtained in the first part of the paper to provide a matrix theoretic proof of a theorem due to j e cohen math proc cambridge philos soc 86 1979 343 350 which states that for an essentially nonnegative and irreducible matrix a the perron root is a convex function of the main diagonal of a

a lower bound for the perron root of a nonnegative matrix ii abstract this paper is a continuation of an earlier one by the author we obtain a new lower bound for the perron root r a of a nonnegative n n matrix a we show that for a with at least one principal submatrix of order two with different diagonal entries and with at least one positive off diagonal entry the bound is at least as good as the one from 7 and we determine a class of nonnegative matrices for which it is essentially better we also show that not every nonnegative square matrix is similar to a nonnegative square matrix with identical diagonal entries

the best possible lower bound for the perron root using traces abstract let a be an n n matrix with real eigenvalues wolkowicz and styan presented bounds for the eigenvalues using only n tr a and tr a 2 we show that their lower bound for the largest eigenvalue works also as a lower bound for the perron root of a if a is nonnegative and its eigenvalues are not necessarily real we also show that this bound is optimal under certain conditions finally we solve completely the problem to find the optimal lower bound for the perron root using only n tr a and tr a 2

the numerical range of 3 3 matrices abstract let a be an n n complex matrix then the numerical range of a w a is defined to be x ax x c n x x 1 in this article a series of tests is given allowing one to determine the shape of w a for 3 3 matrices reconstruction of a up to unitary similarity from w a is also examined

numerical ranges and gersgorin discs abstract for a complex matrix a a ij i j 1 n let w a be its numerical range and let g a be the convex hull of i 1 n z c z a ii i j a ij a ji 2 and g a g u au u n by n unitary it is known that w a is always contained in g a and hence in g a in this paper we consider conditions for w a to be equal to g a or g a we show that if w a g a then the boundary of w a consists only of circular arcs and line segments if moreover a is unitarily irreducible then w a is a circular disc almost complete characterizations of 2 by 2 and 3 by 3 matrices a for which w a g a are obtained we also give criteria for the equality of w a and g a in particular such a s among the permutationally irreducible ones must have even sizes we also characterize those a s with size 2 or 4 which satisfy w a g a

sequences of bounds for the spectral radius of a positive operator abstract in 1992 szyld provided a sequence of lower bounds for the spectral radius of a nonnegative matrix a based on the geometric symmetrization of powers of a in 1998 tasci and kirkland proved a companion result by giving a sequence of upper bounds for the spectral radius of a based on the arithmetic symmetrization of powers of a in this note we extend both results to positive operators on l 2 spaces

bounds on the generalized and the joint spectral radius of hadamard products of bounded sets of positive operators on sequence spaces abstract recently audenaert 2010 2 horn and zhang 2010 15 huang 2011 16 and schep 2011 22 23 proved inequalities between the spectral radius of hadamard product denoted by of finite and infinite non negative matrices that define operators on sequence spaces and the spectral radius of their ordinary matrix product we extend these results to the generalized and the joint spectral radius of bounded sets of such operators moreover we prove new inequalities even in the case of the usual spectral radius of non negative matrices in particular we prove that a b 1 2 a a b b ab ab 1 4 ba ba 1 4 ab and a b 1 2 ab ba ab ab 1 4 ba ba 1 4 ab we also obtain related results in max algebra

tight bounds on the spectral radius of asymmetric nonnegative matrices abstract for an arbitrary asymmetric nonnegative n n matrix a we identify a pair of symmetric matrices whose largest eigenvalues bound the spectral radius of a furthermore we show that these bounding matrices are best possible by characterizing matrices a which attain equality with either the upper or the lower bounding matrix the lower bound may be extended to some matrices with negative entries provided they have no negative cycles

circularity of the numerical range abstract an equivalent condition on a 3 square complex or a 4 square real upper triangular matrix is found for its numerical range to be a circular disk centered at the origin sufficient conditions for the circularity of the numerical range of certain sparse matrices are also given in terms of graphs

numerical ranges of weighted shift matrices abstract we show that if a is an n by n n 3 matrix of the form 0 a 1 0 a n 1 a n 0 then the boundary of its numerical range contains a line segment if and only if the a j s are nonzero and the numerical ranges of the n 1 by n 1 principal submatrices of a are all equal for n 3 this is the case if and only if a 1 a 2 a 3 0 in which case w a the numerical range of a is the equilateral triangular region with vertices the three cubic roots of a 1 a 2 a 3 for n 4 the condition becomes a 1 a 3 0 and a 2 a 4 0 in which case w a is the convex hull of two degenerate or otherwise ellipses

a decreasing sequence of upper bounds for the perron root abstract we obtain a decreasing sequence of upper bounds for the perron root of a nonnegative matrix these upper bounds are new and readily computable for any nonnegative matrix with zero trace the mentioned sequence converges to the perron root we apply these results to the adjacency matrix of a graph

on convexity properties of the spectral radius of nonnegative matrices abstract elementary matrix theoretic proofs are given for the following well known results r d max re an eigenvalue of a d and s d ln e d a are convex here d is diagonal a a nonnegative n n matrix and the spectral radius

perron root bounding for nonnegative persymmetric matrices the eigenvalue problem for a symmetric persymmetric matrix can be reduced to two symmetric eigenvalue problems of lower order in this paper we find in which of these problems the perron root of a nonnegative symmetric persymmetric matrix lies this is applied to bound the perron root of such class of matrices

numerical range of a doubly stochastic matrix abstract we discuss the numerical range of a doubly stochastic matrix and relate it to the structure of the matrix also we characterize those subsets of which are the numerical range of a 3 3 doubly stochastic matrix

an algorithm of diagonal transformation for perron root of nonnegative irreducible matrices abstract it is always to use diagonal transformation for the estimation of nonnegative matrix s perron root however it is invalid for some matrices or a long distance of bounds generated sometimes so the application of this method is limitation therefore in this paper a condition of a diagonal transformation is researched and a new method is proposed for nonnegative irreducible matrices this method can be used for all nonnegative irreducible matrices and its convergence is proved in theory it is convenient to compute by this method and it is easy to get the precision you wanted it is proved by numerical testing that this method is valid and efficient

perron frobenius type results on the numerical range we present results connecting the shape of the numerical range to intrinsic properties of a matrix a w hena is a nonnegative matrix these results are to a large extent analogous to the perron frobenius theory especially as it pertains to irreducibility and cyclicity in the combinatorial sense special attention is given to polygonal circular and elliptic numerical ranges the main vehicles for obtaining these results are the hermitian and skew hermitian parts of a as well as levinger s transformation aa 1 a a 2002 elsevier science

on matrices with cyclic structure abstract the relations between several necessary conditions for a square complex matrix a to be m cyclic are examined these conditions are known to be equivalent if a is an irreducible nonnegative matrix whose index of imprimitivity is m in particular we find that if the digraph of a contains at least one cycle with nonzero signed length then the following conditions are each equivalent to the m cyclicity of a i a is diagonally similar to e 2 i m a ii all cycles in the digraph of a have signed length an integral multiple of m in the course of our investigations we lay down the groundwork of the theory of cyclically m partite or linearly partite digraphs and characterize these digraphs in terms of the signed lengths of their cycles the characterization of diagonal similarity between matrices in terms of matrix cycle products due to saunders and schneider plays a key role in our development our investigations also lead to a new illuminating conceptual proof for the second part of the frobenius theorem on an irreducible nonnegative matrix the connection between the m cyclicity of a square complex matrix and that of its associated collection of elementary jordan blocks is studied in the second half of this paper in particular for an m cyclic collection u it is found that the problem of determining all m tuples k 1 k m of positive integers for which there exists an m cyclic matrix a in the superdiagonal k 1 k m block form such that u a u is equivalent to determine all row sum vectors of 0 1 matrices that have a prescribed column sum vector and each of whose column vectors has cyclically consecutive equal components as a by product we also obtain an equivalent condition on m given square complex matrices b 1 b m so that there exist complex rectangular matrices a 1 a m that satisfy b j a j a m a 1 a j 1 for j 1 m thus completing the work of flanders for the case m 2

inequalities for the perron root related to levinger s theorem abstract for the perron roots of square nonnegative matrices a b and a d 1btd where d is a diagonal matrix with positive diagonal entries the inequality a d 1btd a b is proved under the assumption that a and b have a common unordered pair of nonorthogonal right and left perron vectors the case of equality is analyzed the above inequality generalizes the inequality a 1 bt a 1 b proved under stronger assumptions by bapat and implies a generalization of levinger s theorem on the monotonicity of the perron root of a weighted arithmetic mean of a nonnegative matrix and its transpose also for the perron root a c d 1atd c c 1 0 c of a weighted entrywise geometric mean of a and d 1atd where a ij and o denotes the hadamard product the monotonicity property dual to that asserted by generalized levinger s theorem is established

geometry of the numerical range of matrices abstract some techniques for the study of the algebraic curve c a which generates the numerical range w a of an n n matrix a as its convex hull are developed these enable one to give an explicit point equation of c a and a formula for the curvature of c a at a boundary point of w a applied to the case of a nonnegative matrix a a simple relation is found between the curvature of the function a p 1 a a t p being the perron root at 1 2 and the curvature of w a at the perron root of 1 2 a a t a connection with 2 dimensional pencils of hermitian matrices is mentioned and a conjecture formulated

condition for the numerical range to contain an elliptic disc for an n by n matrix a and an elliptic disc e in the plane we show that the sum of the number of common supporting lines and the number of common intersection points to e and the numerical range w a of a should be at least 2n 1 in order to guarantee that e be contained in w a this generalizes previous results of anderson and thompson as an application our result is used to verify a special case of the poncelet property conjecture 2003 elsevier science inc all rights reserved

high order positivity preserving kinetic schemes for the compressible euler equations we present a new class of high order kinetic flux splitting schemes for the compressible euler equations and we prove that these schemes are positivity preserving i e rho and t remain geq 0 the first order kinetic scheme is based on the maxwellian equilibrium function and was initially proposed by pullin j comput phys 34 1980 pp 231 244 our higher order extension can be seen as a variant of the corrected antidiffusive flux approach the necessity of a limitation on the antidiffusive correction appears naturally in order to satisfy the constraint of positivity

the envelope of tridiagonal toeplitz matrices and block shift matrices abstract the envelope of a square complex matrix is a spectrum encompassing region in the complex plane it is contained in and is akin to the numerical range in the sense that the envelope is obtained as an infinite intersection of unbounded regions contiguous to cubic curves rather than half planes in this article the geometry and properties of the envelopes of special matrices are examined in particular symmetries of the envelope of a tridiagonal toeplitz matrix are obtained and the envelopes of block shift matrices jordan blocks and 2 2 matrices are explicitly characterized

on the spectral radius of positive operators on banach sequence spaces abstract let k 1 k n be infinite non negative matrices that define operators on a banach sequence space given a function f 0 0 0 of n variables we define a non negative matrix f k 1 k n and consider the inequality r f k 1 k n 1 n r k 1 r k n where r denotes the spectral radius we find the largest function f for which this inequality holds for all k 1 k n we also obtain an infinite dimensional extension of the result of cohen asserting that the spectral radius is a convex function of the diagonal entries of a non negative matrix

some monotonicity properties of schur powers of matrices and related inequalities abstract a series of inequalities are developed relating the spectral radius a b of the schur product a b of two nonnegative matrices a and b with those of a a and b b yielding a b a a b b 1 2 as a corollary it is proved that the spectral radius of the schur powers r a r a r a a a r factors satisfies 1 r log r is decreasing while 1 r 1 log r is increasing the latter provided a is a stochastic matrix the entropy of a finite stationary markov chain is identified with d r dr r 1 a number of majorization comparisons for the spectral radius of schur powers is given

comparison theorems for weak splittings of bounded operators comparison theorems for weak splittings of bounded operators are presented these theorems extend the classical comparison theorem for regular splittings of matrices by varga the less known result by wo nicki and the recent results for regular and weak regular splittings of matrices by neumann and plemmons elsner and lanzkron rose and szyld the hypotheses of the theorems presented here are weaker and the theorems hold for general banach spaces and rather general cones hypotheses are given which provide strict inequalities for the comparisons it is also shown that the comparison theorem by alefeld and volkmann applies exclusively to monotone sequences of iterates and is not equivalent to the comparison of the spectral radius of the iteration operators

inequalities of rayleigh quotients and bounds on the spectral radius of nonnegative symmetric matrices abstract given a square nonnegative symmetric matrix a the rayleigh quotient of a nonnegative vector u under a is given by q a u u t au u t u we show that qa u au is not less than qa u where denotes coordinatewise square roots and is the hadamard product but that qa au may be smaller than qa u further we examine issues of convergence

a lower bound for the spectral radius of a digraph abstract we show that the spectral radius d of a digraph d with n vertices and c 2 closed walks of length 2 satisfies d c 2 n moreover equality occurs if and only if d is the symmetric digraph associated to a c 2 n regular graph plus some arcs that do not belong to cycles as an application of this result we construct new sharp upper bounds for the low energy of a digraph which extends koolen and moulton bounds of the energy to digraphs

bounds for the spectral radius and the largest singular value abstract we derive an increasing sequence of lower bounds for the spectral radius of a matrix with real spectrum and progressively improved bounds for the largest singular value of a complex matrix we also find estimates for the rank of normal matrices with real spectrum and for the rank of normal nonnegative matrices including some sufficient condition for such matrices to be invertible

kinetic symmetrizations and pressure laws for the euler equations abstract the symmetrizations of the compressible euler equations written as kinetic mean are studied some of their properties are pointed out we emphasize for numerical purpose the case of real rarefied gases with pressure laws p f flux splitting formulae are derived for such pressure laws

new developments in kinetic schemes kinetic schemes for the numerical solution of pde of fluid dynamics are a new class of upwind schemes the moment method strategy used in constructing these schemes is based on the connection between the boltzmann equation of kinetic theory of gases and governing equations of fluid dynamics any upwind scheme for the solution of the boltzmann equation becomes an upwind scheme for the solution of pde of fluid dynamics by taking suitable moments this idea has been exploited in the present paper in developing least squares kinetic upwind method lskum and kinetic flux vector splitting method on moving grid kfmg the robustness and versatility of lskum has been demonstrated by applying it to 2 d flow problems of inviscid gas dynamics the lskum has been found to operate on any type of grid and can be called a grid fault tolerant scheme in view of the use of least squares approximation to the space derivatives the kfmg is a promising new method showing how easily the kinetic schemes lend themselves easily to problems involving moving grids which are generally employed while solving problems in unsteady aerodynamics