a necessary and sufficient condition for m matrices and its relation to block lu factorization abstract we present a necessary and sufficient condition for m matrices in terms of a special diagonal dominance then we use the new result to show that if the block comparison matrix of a block matrix a is an m matrix there exists a block permutation matrix p such that block lu factorization applied to a p t a p is stable i e the norms of the block multipliers a k 1 i k a k 1 k k are bounded by 1 we also present a collection of tools in the literature related to the subject matter we define incomplete m matrices prove a necessary and sufficient condition for such matrices and present their implications for block lu factorization

locally connected models for julia sets let p be a polynomial with a connected julia set j we use continuum theory to show that it admits a finest monotone map onto a locally connected continuum j p i e a monotone map j j p such that for any other monotone map j j there exists a monotone map h with h then we extend onto the complex plane c keeping the same notation and show that monotonically semiconjugates p c to a topological polynomial g c c if p does not have siegel or cremer periodic points this gives an alternative proof of kiwi s fundamental results on locally connected models of dynamics on the julia sets but the results hold for all polynomials with connected julia sets we also give a characterization and a useful sufficient condition for the map not to collapse all of j into a point

some results on sparse block factorization iterative methods abstract we consider the general sparse block factorization iterative methods as beauwens and ben bouzid did we develop some existence and convergence theorems for general nonsingular h matrices

on schur complement of block diagonally dominant matrices abstract it is well known that the schur complements of strictly diagonally dominant matrices are strictly diagonally dominant d carlson t markham schur complements of diagonally dominant matrices czech math j 29 104 1979 246 251 the same is true of generalized strictly diagonally dominant matrices jianzhou liu yungqing huang some properties on schur complements of h matrix and diagonally dominant matrices linear algebra appl 389 2004 365 380 in this paper this result is extended to the block strictly diagonally dominant matrices and the generalized block strictly diagonally dominant matrices that is it is shown that the schur complement of a block strictly diagonally dominant matrix is a block strictly diagonally dominant matrix and so is the schur complement of a generalized block strictly diagonally dominant matrix

block ilu factorization preconditioners for a block tridiagonal h matrix abstract we propose new parallelizable block ilu incomplete lu factorization preconditioners for a nonsymmetric block tridiagonal h matrix theoretical properties of these block ilu preconditioners are compared with those of block ilu preconditioners for the corresponding comparison matrix numerical results of the bicgstab using these block preconditioners are compared with those of the bicgstab using a standard ilu factorization preconditioner to see the effectiveness of the block ilu preconditioners lastly parallel computations of the block ilu preconditioners are carried out and evaluated on the cray c90

incomplete blockwise factorizations of block h matrices the use of incomplete blockwise factorizations as preconditioners in conjugate gradient like methods has become more and more popular in recent years most of the theory concerning existence and applicability of these factorizations has been limited to m matrices so far here we introduce a more general definition of block h matrices robert 8 and we extend the theory to this class of matrices

a general incomplete block matrix factorization method abstract a general method for incomplete factorization of m matrices in block matrix form is presented the method generalizes previous methods for pointwise incomplete factorization methods of varga 1960 of wo nicki 1973 and of meijerink and van der vorst 1977 as well as a method for tridiagonal block matrices also we present a new and more general result on the existence of so called modified incomplete factorizations which satisfy a generalized rowsum criterion

on the stability of the incomplete lu factorizations and characterizations of h matrices meijerink and van der vorst 8 have shown that the incomplete lu factorizations are numerically stable for m matrices varga saff and mehrmann 16 gave some characterizations of the h matrices by using the incomplete lu factorizations of them the purpose of this paper is to show that the incomplete lu factorizations of an h matrix are at least as stable as the complete lu factorizations of its comparison matrix we give also some new characterizations of the h matrices in connection with their incomplete lu factorizations

on some versions of incomplete block matrix factorization iterative methods abstract various forms of preconditioning matrices for iterative acceleration methods are discussed the preconditioning is based on two versions of incomplete block matrix factorization

a framework for block ilu factorizations using block size reduction the authors propose a block ilu factorization technique for block tridiagonal matrices that need not necessarily be m matrices the technique explores reduction by a coarse vector restriction of the block size of the approximate schur complements computed throughout the factorization process then on the basis of the sherman morrison woodbury formula these are easily inverted they prove the existence of the proposed factorization techniques in the case of nonsymmetric in general m matrices for block tridiagonal matrices with positive definite symmetric part they show the existence of a limit version of the factorization exact inverses of the reduced matrices are needed the theory is illustrated with numerical tests 24 refs 9 tabs

weak block diagonally dominant matrices weak block h matrix and their applications abstract here we introduce more general definitions of weak block diagonally dominant matrix and weak block h matrix which permit block triangular factorizations and extend the theory to the block diagonally dominant matrices and the block h matrices furthermore by the theory of weak block h matrix we prove that any partitioned block form of a pointwise h matrix has a block triangular factorization

on asynchronous iterations asynchronous iterations arise naturally on parallel computers if one wants to minimize idle times this paper reviews certain models of asynchronous iterations using a common theoretical framework the corresponding convergence theory and various domains of applications are presented these include nonsingular linear systems nonlinear systems and initial value problems

twice punctured hyperbolic sphere with a conical singularity and generalized elliptic integral we describe in terms of generalized elliptic integrals the hyperbolic metric of the twice punctured sphere with one conical singularity of prescribed order we also give several monotonicity properties of the metric and a couple of applications

letter to the editor a simple estimation for the spectral radius of block h matrices simple bounds for the spectral radius of an h matrix and a block h matrix are presented respectively i e a 2maxi aii for an h matrix a aij and a maxi aii aii 1 for a block h matrix a aij where a denote the spectral radius

metrics with conical singularities on the sphere and sharp extensions of the theorems of landau and schottky an explicit formula for the generalized hyperbolic metric on the thrice punctured sphere mathbb p backslash z 1 z 2 z 3 with singularities of order j 1 at zj is obtained in all possible cases 1 2 3 2 the existence and uniqueness of such a metric was proved long time ago by picard j reine angew math 130 243 258 1905 and heins nagoya math j 21 1 60 1962 while explicit formulas for the cases 1 2 1 were given earlier by agard ann acad sci fenn ser a i 413 1968 and recently by anderson et al math z to appear doi 10 1007 s00209 009 0560 5 we also establish precise and explicit lower bounds for the generalized hyperbolic metric this extends work of hempel j lond math soc ii ser 20 435 445 1979 and minda complex var 8 129 144 1987 as applications sharp versions of landau and schottky type theorems for meromorphic functions are obtained

criterion for rays landing together let f be a polynomial with degree 2 and the julia set j f locally connected we give a partition of complex plane c and show that if z z in j f have the same itinerary respect to the partition then either z z or both of them lie in the boundary of a fatou component u which is eventually iterated to a siegel disk as an application we prove the monotonicity of core entropy for the quadratic polynomial family fc z 2 c fc has no siegel disks and j fc is locally connected

real laminations and the topological dynamics of complex polynomials abstract we characterize the laminations associated to complex polynomials with connected julia sets and without irrationally neutral cycles

inverse h matrices abstract the notion of inverse m matrices has been quite well studied and many of their properties have been documented in the literature in this article a proposal to consider the larger class of inverse h matrices is made first certain special types of real matrices are identified as inverse h matrices while these matrices are not inverse m matrices in general their definitions are inspired by matrices that are known to be inverse m matrices in the rest of the article motivated by results that hold for inverse m matrices the endeavor will be to attempt at proving corresponding results for inverse h matrices it is shown that for the full class of inverse h matrices many of these extensions are false nevertheless two subclasses of real inverse h matrices are identified where these generalizations are shown to hold

on the isolated singularities of the solutions of the gaussian curvature equation for nonnegative curvature abstract the precise asymptotic behaviour of the solutions to the two dimensional curvature equation u k z e 2 u with e 2 u l 1 for bounded nonnegative curvature functions k z near isolated singularities is obtained

a core decomposition of compact sets in the plane abstract a peano continuum means a locally connected continuum a compact metric space is called a peano compactum if all its components are peano continua and if for any constant c 0 all but finitely many of its components are of diameter less than c given a compact set k c there usually exist several upper semi continuous decompositions of k into subcontinua such that the quotient space equipped with the quotient topology is a peano compactum we prove that one of these decompositions is finer than all the others and call it the core decomposition of k with peano quotient this core decomposition gives rise to a metrizable quotient space called the peano model of k which is shown to be determined by the topology of k and hence independent of the embedding of k into c we also construct a concrete continuum k r 3 such that the core decomposition of k with peano quotient does not exist for specific choices of k c the above mentioned core decomposition coincides with two models obtained recently namely the locally connected model for unshielded planar continua like connected julia sets of polynomials and the finitely suslinian model for unshielded planar compact sets like polynomial julia sets that may not be connected the study of such a core decomposition provides partial answers to several questions posed by curry in 2010 these questions are motivated by other works including those by curry and his coauthors that aim at understanding the dynamics of a rational map f c c restricted to its julia set

wandering orbit portraits we study a counting problem in holomorphic dynamics related to external rays of complex polynomials we give upper bounds on the number of external rays that land at a point z in the julia set of a polynomial provided that z has an infinite forward orbit

rigidity and non local connectivity of julia sets of some quadratic polynomials for an infinitely renormalizable quadratic map f c z mapsto z 2 c with the sequence of renormalization periods km and rotation numbers tm pm qm we prove that if limsup k m 1 log p m 0 then the mandelbrot set is locally connected at c we prove also that if limsup t m 1 1 q m 1 and qm then the julia set of fc is not locally connected and the mandelbrot set is locally connected at c provided that all the renormalizations are non primitive satellite this quantifies a construction of a douady and j hubbard and weakens a condition proposed by j milnor

on local connectivity for the julia set of rational maps newton s famous example we show that newton s cubic methods famous rational maps have a locally connected julia set except in some very specific cases in particular when those maps are infinitely renormalizable their julia set is locally connected and contains small copies of nonlocally connected quadratic julia sets this also holds when newton s method is renormalizable and has cremer points unlike the polynomial case after a dynamical description we show the necessity of the brjuno condition within this family

on the existence of block diagonal solutions to lyapunov and mathcal h _ infty riccati inequalities in this note we describe sufficient conditions when block diagonal solutions to lyapunov and mathcal h infty riccati inequalities exist in order to derive our results we define a new type of comparison systems which are positive and are computed using the state space matrices of the original possibly nonpositive systems computing the comparison system involves only the calculation of mathcal h infty norms of its subsystems we show that the stability of this comparison system implies the existence of block diagonal solutions to lyapunov and riccati inequalities furthermore our proof is constructive and the overall framework allows the computation of block diagonal solutions to these matrix inequalities with linear algebra and linear programming numerical examples illustrate our theoretical results

a convergence analysis of block accelerated over relaxation iterative methods for weak block h matrices to partition π abstract the aim of this paper is to establish the convergence of the block iteration methods such as the block successively accelerated over relaxation method baor and the symmetric block successively accelerated over relaxation method bsaor let a c n m m be a weak block h matrix to partition then for 0 r 2 1 b j a b l r 1 b j a b s r 1 b j a 2 and exact convergence and divergence domains for the block sor and block ssor iterative methods are obtained as it has been obtained to h matrices based on these results the main results in bai parallel computing 25 1999 and cvetkovic appl numer math 41 2002 can be improved

an extended fatou shishikura inequality and wandering branch continua for polynomials abstract let p be a polynomial of degree d with julia set j p let n be the number of non repelling cycles of p by the famous fatou shishikura inequality n d 1 the goal of the paper is to improve this bound the new count includes wandering collections of non pre critical branch continua i e collections of continua or points q i j p all of whose images are pairwise disjoint contain no critical points and contain the limit sets of eval q i 3 external rays also we relate individual cycles which are either non repelling or repelling with no periodic rays landing to individual critical points that are recurrent in a weak sense a weak version of the inequality reads n n irr i eval q i 2 d 1 where n irr counts repelling cycles with no periodic rays landing at points in the cycle q i form a wandering collection b c of non pre critical branch continua 1 if b c is non empty and 0 otherwise

stability of block lu factorization for block tridiagonal block h matrices by a block representation of lu factorization for a general matrix introduced by amodio and mazzia p amodio f mazzia a new approach to the backward error analysis in the lu factorization algorithm bit 39 1999 385 402 a block representation of block lu factorization for block tridiagonal block h matrices is obtained and some properties on the factors of the factorization are presented perturbation theory for the block lu factorization of block tridiagonal block h matrices is also considered then a rounding error analysis of the block lu factorization for block tridiagonal block h matrices is given and some bounds for the growth factor are proposed finally a numerical example is presented to illustrate our theoretical results

laminations in the language of leaves thurston defined invariant laminations i e collections of chords of the unit circle s called leaves that are pairwise disjoint inside the open unit disk and satisfy a few dynamical properties to be directly associated to a polynomial a lamination has to be generated by an equivalence relation with specific properties on s then it is called a q lamination since not all laminations are q laminations then from the point of view of studying polynomials the most interesting are those of them which are limits of q laminations in this paper we introduce an alternative definition of an invariant lamination which involves only conditions on the leaves and avoids gap invariance the new class of laminations is slightly smaller than that defined by thurston and is closed we use this notion to elucidate the connection between invariant laminations and invariant equivalence relations on s

isolated singularities of affine special kahler metrics in two dimensions we prove that there are just two types of isolated singularities of special kahler metrics in real dimension two provided the associated holomorphic cubic form does not have essential singularities we also construct examples of such metrics

stability of block lu factorization for block tridiagonal matrices it is showed that if a is i block diagonally dominant ii block diagonally dominant then the reduced matrix s preserves the same property we also give a sufficient condition for the reduced matrix s also to be a block h matrix when a is a block h matrix and some properties on the comparison matrices m i a k m i i a k m i l and m i u are obtained finally error analysis of block lu factorization for block tridiagonal matrix is presented

the iteration of cubic polynomials part i the global topology of parameter space fonctions univalentes en dynamique analytique complexe torsion de la structure complexe topologie globale de l espace parametre

on incomplete block factorization methods of generalized ssor type for h matrices abstract two types of modified incomplete block factorization methods are considered and the existence and convergence of the related splittings are established for h matrices this is done by studying in parallel the similar preconditioner for an m matrix a which satisfies a m a we show also for the m matrix case somewhat more general results for the type of preconditioners considered than previously found in the literature

a class of parallel decomposition type relaxation methods for large sparse systems of linear equations abstract a class of parallel decomposition type accelerated over relaxation methods including four arbitrary parameters and suitable to the simd systems is established for solving the large sparse systems of linear equations in this paper and sufficient conditions ensuring its convergence are deduced when the coefficient matrices of the linear systems of equations are respectively l matrices h matrices and positive definite matrices in particular we investigate in detail the symmetric versions of these new methods and deduce a series of conveniently applicable conditions for determining the convergence of hese versions when the coefficient matrices of the linear systems of equations are symmetric positive definite matrices

theorems on schur complement of block diagonally dominant matrices and their application in reducing the order for the solution of large scale linear systems abstract we firstly consider the block dominant degree for i ii block strictly diagonally dominant matrix and their schur complements showing that the block dominant degree for the schur complement of an i ii block strictly diagonally dominant matrix is greater than that of the original grand block matrix then as application we present some disc theorems and some bounds for the eigenvalues of the schur complement by the elements of the original matrix further by means of matrix partition and the schur complement of block matrix based on the derived disc theorems we give a kind of iteration called the schur based iteration which can solve large scale linear systems though reducing the order by the schur complement and the numerical example illustrates that the iteration can compute out the results faster

prescribing curvature on compact surfaces with conical singularities we study the berger nirenberg problem on surfaces with conical singularities i e we discuss conditions under which a function on a riemann surface is the gaussian curvature of some conformal metric with a prescribed set of singularities of conical types