basic soules matrices and their applications abstract in this paper we study the properties of the basic soules matrices in r n n which are a special subclass of the n n soules matrices generated via the basic soules basis the basic soules basis has the sign pattern n and it corresponds to the vector e n r n of all 1 s the basic soules matrices are up to a multiple by a positive scalar symmetric and doubly stochastic we begin by investigating the permanents of basic soules matrices next for a nonsingular basic soules matrix a r n n we show that the matrix a a 1 which is known to be a nonsingular m matrix has a basic soules basis of eigenvectors furthermore we obtain explicit formulas for the eigenvalues of a a 1 in terms of the eigenvalues of a finally let a r n n be a basic soules matrix of spectral radius 1 and set q i a by investigating the sign pattern of the off diagonal entries of the group inverse q of q we determine when the perron root is a concave function in each of the off diagonal entries at a

an efficient iterative method for solving bratu type equations abstract in this paper an efficient analytical iterative method is introduced for solving the initial value and boundary value bratu problems a quasilinearization method with an optimal parameter is derived and utilized to reduce the highly nonlinear bratu equations to a sequence of linear problems an optimal picard iteration method is used to obtain approximate analytical solution of linearized versions of bratu s equations the numerical results presented the effectiveness and high performance of the proposed method and comparisons are made with many other existing numerical solution techniques the comparisons reveal the efficiency and applicability of the present work

on the second real eigenvalue of nonegative and z matrices abstract we give bounds for the second real eigenvalue of nonegative matrices and z matrices furthermore we establish upper bounds for the maximal spectral radii of principal submatrices of nonnegative matrices using these bounds we prove that our inequality for the second real eigenvalue of the adjacency matrix of a connected regular graph improves a well known bound for the second eigenvalue using cheeger s inequality

a generalization of n matrices abstract ky fan defines an n matrix to be a matrix of the form a ti b b 0 t b where b is the spectral radius of b and is the maximum of the spectral radii of all principal submatrices of b of order n 1 in this paper we define the closure n 0 matrices of n matrices by letting t it is shown that if a z and a 1 a n certain inequalities of n matrices are shown to hold for n 0 matrices and a method for constructing an n matrix from an m matrix is given

on single and double soules matrices abstract until now the concept of a soules basis matrix of sign pattern n consisted of an orthogonal matrix r r n n generated in a certain way from a positive n vector which has the property that for any diagonal matrix diag 1 n with 1 n 0 the symmetric matrix a r r t has nonnegative entries only in the present paper we introduce the notion of a pair of double soules basis matrices of sign pattern n which is a pair of matrices p q each in r n n which are not necessarily orthogonal and which are generated in a certain way from two positive vectors but such that pq t i and such that for any of the aforementioned diagonal matrices the matrix a p q t also has nonnegative entries only we investigate the interesting properties which such matrices a have as a preamble to the above investigation we show that the iterates a k r k r k t generated in the course of the qr algorithm when it is applied to a r r t where r is a soules basis matrix of sign pattern n are again symmetric matrices generated by the soules basis matrices r k of sign pattern n which are themselves modified as the algorithm progresses our work here extends earlier works by soules and elsner et al

inverse no matrices abstract results similar to those of thomas l markham concerning inverse m matrices are shown to hold for inverse n o matrices a more general result and an alternate method of proof using schur complements are given for one of markham s theorems conditions are given to transform a nonpositive matrix to an n o amtrix by multiplication by householder transformations also an lu factorization of an inverse n o matrix is given

the partial order graph for a zme matrix abstract the spectral projectors for a zme matrix form a partially ordered set with respect to a simple combinatorial relation the relationship between the corresponding partial order graph and the inflation sequence for a set of projectors is investigated those directed graphs that correspond to a partial order graph for a zme matrix are characterized the effect on the partial order due to operations on the set of projectors is studied generalizing a result of schneider and stuart

numerical solution of evolution equations by the haar wavelet method an efficient numerical method for solution of nonlinear evolution equations based on the haar wavelets approach is proposed the method is tested in the case of burgers and sine gordon equations numerical results obtained by computer simulation are compared with other available solutions these calculations demonstrate that the accuracy of the haar wavelet solutions is quite high even in the case of a small number of grid points

a conjecture concerning the hadamard product of inverses of m matrices abstract we conjecture that for an n n matrix a which is an inverse of an m matrix the hadamard product a a is also an inverse of an m matrix we have checked this conjecture without failure on many many examples but here we show that for quite a few well known classes of inverses of m matrices the conjecture is true it is known that the more general conjecture that when a and b are n n inverses of m matrices then a b is also an inverse of an m matrix is false however here too we are able to display some classes of inverses of m matrices which are closed under taking hadamard products

on the minus partial order in control systems abstract in this paper the minus matrix partial order is considered to introduce the concept of minus partial ordered control systems the transmission of the reachability property under this binary relation is investigated furthermore the analysis of compartmental systems leads us to consider block triangular matrices hence the existence and computation of partially ordered matrices having a similar block structure are studied these results are applied to compartmental systems to get via feedback related systems with the same block structure and ordered under the minus partial order

adomian decomposition method for a reliable treatment of the bratu type equations in this paper we present a framework to determine exact solutions of bratu type equations the algorithm rests mainly on the adomian decomposition method the proposed scheme is illustrated by studying two boundary value problems and an initial value problem of bratu type the first type gives a solution that blows up at the middle of the domain whereas the other equations give bounded solutions

legendre wavelets method for solving differential equations of lane emden type a numerical method for solving the lane emden equations as singular initial value problems is presented using integral operator and convert lane emden equations to integral equations and then applying legendre wavelet approximations the properties of legendre wavelet are first presented these properties together with the gaussian integration method are then utilized to reduce the integral equations to the solution of algebraic equations illustrative examples are included to demonstrate the validity and applicability of the technique

the legendre wavelet method for solving initial value problems of bratu type the aim of this work is to study the legendre wavelets for the solution of initial value problems of bratu type which is widely applicable in fuel ignition of the combustion theory and heat transfer the properties of legendre wavelets together with the gaussian integration method are used to reduce the problem to the solution of nonlinear algebraic equations also a reliable approach for convergence of the legendre wavelet method when applied to a class of nonlinear volterra equations is discussed and an error estimation for the proposed method is also introduced illustrative examples have been discussed to demonstrate the validity and applicability of the technique and the results have been compared with the exact solution we finally show the high accuracy and efficiency of the proposed method

on integral representation of the generalized inverse at s 2 we present a general integral representation for the generalized inverse a t s 2 which extends earlier result on the moore penrose inverse weighted moore penrose inverse and drazin inverse

eigenvalue location for nonnegative and z matrices let lk0 denote the class of n n z matrices a tl b with b 0 and k b t k 1 b where k b denotes the maximum spectral radius of k k principal submatrices of b bounds are determined on the number of eigenvalues with positive real parts for a lk0 where k satisfies n2 k n 1 for these classes when k n 1 and n 2 wedges are identified that contain only the unqiue negative eigenvalue of a these results lead to new eigenvalue location regions for nonnegative matrices

special families of matrices a talk in honor of miroslav fiedler abstract this paper is essentially the talk that i delivered in the minisymposium in honor of miroslav fiedler at the 17th ilas meeting in braunschweig germany

on classes of inverse z matrices abstract recently a classification of matrices of class z was introduced by fiedler and markham this classification contains the classes of m matrices and the classes of n 0 and f 0 matrices studied by fan g johnson and smith the problem of determining which nonsingular matrices have inverses which are z matrices is called the inverse z matrix problem for special classes of z matrices such as the m and n 0 matrices there exist at least partial results i e special classes of matrices have been introduced for which the inverse of such a matrix is an m matrix or an n 0 matrix here we define a system of classes of matrices for which the inverse of each matrix of each class belongs to one class of the classification of z matrices defined by fiedler and markham moreover certain properties of the matrices of each class are established e g inequalities for the sum of the entries of the inverse and the structure of certain schur complements we also give a necessary and sufficient condition for regularity the class of inverse n 0 matrices given here generalizes the class of inverse n 0 matrices discussed by johnson all results established here can be applied to a class of distance matrices which corresponds to a nonarchimedean metric this metric arises in p adic number theory and in taxonomy

characteristic finite element methods for diffusion epidemic models with age structured populations a numerical approximation is considered for a model of epidemiology describing age dependent population dynamics with spatial diffusion a finite difference method along the characteristic age time direction is combined with finite elements in the spatial variable optimal order error estimates are derived for the approximation

some results on a partition of z matrices fiedler and markham define an n n matrix a to be an lk matrix if a has the form a ti b where b is nonnegative and k b t k 1 b k 1 2 n here k b denotes the maximum spectral radius of all principal submatrices of b of order k for k 1 2 n and for completeness n 1 b is defined to be further a is defined to be an l0 matrix if a ti b where b is nonnegative and t 1 b the classes l0 l1 ln form a partition of the class of z matrices in this paper we characterize nonsingular matrices in these classes in terms of the principal minors of their inverses and extend this characterization to general lk matrices inverse lk matrices and schur complements of lk matrices are also studied an eigenvalue inequality involving schur complements of lk matrices is obtained

the symmetric nonnegative inverse eigenvalue problem for 5 5 matrices abstract the symmetric nonnegative inverse eigenvalue problem sniep asks when a list 1 2 n of n real numbers is the spectrum of an n n symmetric nonnegative matrix this problem is completely solved only for n 4 our main goal here is to contribute to the solution of sniep for n 5 we also give a sufficient condition for a list to be realized as the spectrum of a symmetric positive matrix

characterizations of mma matrices abstract in a recent paper s friedland d hershkowitz and h schneider characterized among other classes the mma matrices i e real square matrices all of whose positive powers are irreducible m matrices by finding a recursive property allowing one to express such a matrix using mma matrices of smaller order in this paper we add several characterizations which do not refer to mma matrices of smaller order and answer thus a problem raised in 2

on perron complements of inverse n0 matrices abstract in this paper we show that the perron complements of irreducible n 0 matrices are n 0 matrices we also demonstrate the perron complements of irreducible inverse n 0 matrices are inverse n 0 matrices with a little restriction in addition we give some related inequalities about inverse n 0 matrices

an algorithm for determining if the inverse of a strictly diagonally dominant stieltjes matrix is strictly ultrametric it was recently shown that the inverse of a strictly ultrametric matrix is a strictly diagonally dominant stieltjes matrix on the other hand as it is well known that the inverse of a strictly diagonally dominant stieltjes matrix is a real symmetric matrix with nonnegative entries it is natural to ask conversely if every strictly diagonally dominant stieltjes matrix has a strictly ultrametric inverse examples show however that the converse is not true in general i e there are strictly diagonally dominant stieltjes matrices in n n for everyn 3 whose inverses are not strictly ultrametric matrices then the question naturally arises if one can determine which strictly diagonally dominant stieltjes matrices in n n n 3 have inverses which are strictly ultrametric here we develop an algorithm based on graph theory which determines if a given strictly diagonally dominant stieltjes matrixa has a strictly ultrametric inverse where the algorithm is applied toa and requires no computation of inverse moreover if this given strictly diagonally dominant stieltjes matrix has a strictly ultrametric inverse our algorithm uniquely determines this inverse as a special sum of rank one matrices

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 the inverse mean first passage matrix problem and the inverse m matrix problem abstract the inverse mean first passage time problem is given a positive matrix m r n n then when does there exist an n state discrete time homogeneous ergodic markov chain c whose mean first passage matrix is m the inverse m matrix problem is given a nonnegative matrix a then when is a an inverse of an m matrix the main thrust of this paper is to show that the existence of a solution to one of the problems can be characterized by the existence of a solution to the other in so doing we extend earlier results of tetali and fiedler

a modularity based spectral method for simultaneous community and anti community detection abstract in a graph or complex network communities and anti communities are node sets whose modularity attains extremely large values positive and negative respectively we consider the simultaneous detection of communities and anti communities by looking at spectral methods based on various matrix based definitions of the modularity of a vertex set invariant subspaces associated to extreme eigenvalues of these matrices provide indications on the presence of both kinds of modular structure in the network the localization of the relevant invariant subspaces can be estimated by looking at particular matrix angles based on frobenius inner products

a new method for solving singular initial value problems in the second order ordinary differential equations singular initial value problems linear and nonlinear homogeneous and nonhomogeneous are investigated by using adomian decomposition method the solutions are constructed in the form of a convergent series a new general formula is established the approach is illustrated with few examples

inverse m matrices ii this is an update of the 1981 survey by the first author in the meantime a considerable amount has been learned about the very special structure of the important class of inverse m matrices developments since the earlier survey are emphasized but we have tried to be somewhat complete and some results have not previously been published some proofs are given where appropriate and references are given for others after some elementary preliminaries results are grouped by certain natural categories

orthogonal bases that lead to symmetric nonnegative matrices abstract in a paper dating back to 1983 soules constructs from a positive vector x an orthogonal matrix r which has the property that for any nonnegative diagonal matrix with nonincreasing diagonal entries the matrix r rt has all its entries nonnegative independently fiedler in 1988 showed that any symmetric irreducible nonsingular matrix whose powers are all m matrices and hence an mma matrix in the language of friedland hershkowitz and schneider must have an orthogonal matrix of eigenvectors r which has similar properties to those of r here for a given positive n vector x we investigate the structure of all orthogonal matrices r for which for any nonnegative diagonal matrix as above the matrices r rt are nonnegative up to a permutation of its columns each such r corresponds to a binary tree whose vertices are subsets of the set 1 2 n with the property that each vertex has either no successor or exactly two disjoint successors for such orthogonal matrices r and such nonsingular diagonal matrices we show that the set of matrices of the form r rt and the set of inverse mma matrices i e matrices whose inverses are mma matrices coincide using this result we establish a relation between strictly ultrametric matrices and inverse mma matrices finally we show that the qr factorization of r rt for certain such r s has a special sign pattern

generalizations of m matrices which may not have a nonnegative inverse abstract generalizations of m matrices are studied including the new class of gm matrices the matrices studied are of the form si b with b having the perron frobenius property but not necessarily being nonnegative results for these classes of matrices are shown which are analogous to those known for m matrices also various splittings of a gm matrix are studied along with conditions for their convergence

generalized ultrametric matrices a class of inverse m matrices abstract recently marti nez michon and san marti n introduced the new class of symmetric strictly ultrametric matrices they proved that the inverse of a strictly ultrametric matrix is a strictly row and strictly column diagonally dominant stieltjes matrix here we generalize their result by introducing a class of nonsymmetric matrices calledgeneralized ultrametric matrices we give a necessary and sufficient condition for the regularity of these matrices and prove that the inverse of a nonsingular generalized ultrametric matrix is a row and column diagonally dominant m matrix we establish that a nonnegative matrix is a generalized ultrametric matrix if and only if the matrix is a certain sum of at most rank two matrices moreover we give a characterization of generalized ultrametric matrices based on weighted trees the entries of generalized ultrametric matrices then arise as certain distances between the leaves and the root of the tree

chebyshev polynomial expansions for simultaneous approximation of two branches of a function with application to the one dimensional bratu equation we introduce two methods for simultaneously approximating both branches of a two branched function using chebyshev polynomials both schemes remove the pernicious convergence wrecking effects of the square root singularity at the limit point where the two branches meet the chebyshev shafer method gives the approximants as the solution to a quadratic equation the mapping algorithm makes a quadratic change of variable for both the only input information is the set of values of f x at a set of discrete points there is little to choose between the two schemes in accuracy but the single expansion mapping method is more flexible in that it can accommodate different ranges on the two branches the eigenrelation for the one dimensional bratu equation is an interesting example because the upper branch is also singular at another point besides the limit point this too can be removed by subtracting the asymptotic solution which is the lambert w function from the upper branch only when the domain of the variable is infinite the quadratic change of variable can still be applied by substituting rational chebyshev functions which are basis functions for an unbounded interval for chebyshev polynomials we illustrate this by approximating the real valued root of the brill quintic u 5 u l l which was first solved by hermite using elliptic modular functions more than a century ago

characterizations of inverse m matrices with special zero patterns in this paper we provide some characterizations of inverse m matrices with special zero patterns in particular we give necessary and sufficient conditions for k diagonal matrices and symmetric k diagonal matrices to be inverse m matrices in addition results for triadic matrices tridiagonal matrices and symmetric 5 diagonal matrices are presented as corollaries

classes of general h matrices let m a denote the comparison matrix of a square h matrix a that is m a is an m matrix h matrices such that their comparison matrices are nonsingular are well studied in the literature in this paper we study characterizations of h matrices with either singular or nonsingular comparison matrices the spectral radius of the jacobi matrix of m a and the generalized diagonal dominance property are used in the characterizations finally a classification of the set of general h matrices is obtained

mixed approximation of a population diffusion equation abstract a numerical method is proposed to approximate the solution of a nonlinear and nonlocal system of integro differential equations describing age dependent population dynamics with spatial diffusion a finite difference method along the characteristic age time direction combined with mixed finite elements in the spatial variable is used for the approximation optimal order error estimates are derived for the relevant variables using nonnegativity of the discrete solution a stability of the method is also proved

the liouville bratu gelfand problem for radial operators abstract we determine precise existence and multiplicity results for radial solutions of the liouville bratu gelfand problem associated with a class of quasilinear radial operators which includes perturbations of k hessian and p laplace operators

eigenvalue interlacing for certain classes of matrices with real principal minors abstract two common properties of z matrices and hermitian matrices are considered 1 the eigenvalue interlacing property i e the two smallest real eigenvalues of a matrix are interlaced by the smallest real eigenvalue of any principal submatrix of order one less 2 the positive glp property i e if a matrix has a positive sequence of generalized leading principal minors then all the principal minors of the matrix are positive the relationship between these properties as well as related properties is examined in general

an efficient method for solving bratu equations in this paper we present a numerical technique for solving bratu equation it is based on the laplace adomain decomposition method which produces an implicit equation in two variables we used the predictor corrector technique to trace the solution curve generated from this equation numerical results and conclusions will be presented

some notes on z matrices abstract an inequality is obtained relating the eigenvalue of minimum modulus of an n0 matrix a to the eigenvalue of minimum modulus of a a11 the schur complement of a11 in a where a11 is an m matrix similar results are obtained for irreducible m matrices and irreducible nonsingular f0 matrices circulant n0 matrices of order three are characterized in terms of their spectrum matrices whose inverses are f0 matrices are shown to have nonpositive almost principal minors

perron spectratopes and the real nonnegative inverse eigenvalue problem abstract call an n by n invertible matrix s a perron similarity if there is a real non scalar diagonal matrix d such that s d s 1 is entrywise nonnegative we give two characterizations of perron similarities and study the polyhedra c s x r n s d x s 1 0 d x diag x and p s x c s x 1 1 which we call the perron spectracone and perron spectratope respectively the set of all normalized real spectra of diagonalizable nonnegative matrices may be covered by perron spectratopes so that enumerating them is of interest the perron spectracone and spectratope of hadamard matrices are of particular interest and tend to have large volume for the canonical hadamard matrix as well as other matrices the perron spectratope coincides with the convex hull of its rows in addition we provide a constructive version of a result due to fiedler 9 theorem 2 4 for hadamard orders and a constructive version of the boyle handelman theorem 2 theorem 5 1 for sule manova spectra

the decomposition of idempotents associated with inflators abstract in a recent paper friedland hershkowitz and schneider introduced a new matrix product called the inflation product and a new class of matrices called inflators fundamental to the constructions were certain idempotent matrices associated with the inflators this paper studies the structure of the idempotent matrix associated with an inflator in particular it is shown that if the idempotent associated with an inflator has rank greater than one then the idempotent can be split into several pairwise orthogonal idempotents of lower rank such that the resultant idempotents are associated with inflators which are inflation product factors of the original inflator the indecomposable idempotents associated with the decomposition of an inflator are characterized in terms of rank and are shown to be generally nonunique the number of indecomposable idempotents in a splitting is shown to be invariant

schur complements and its applications to symmetric nonnegative and z matrices in linear algebra appl 177 1992 137 smith proved that if h is a hermitian semidefinite matrix and a is a nonsingular principal submatrix then the eigenvalues of the schur complement h a interlace those of h in this paper we refine the latter result and use it to derive eigenvalues interlacing results on an irreducible symmetric nonnegative matrix that involve perron complements for an irreducible symmetric nonnegative matrix we give lower and upper bounds for its spectral radius and also a lower bound for the maximal spectral radius of its principal submatrices of a fixed order we apply our results to an irreducible symmetric z matrix and to the adjacency matrix or the general laplacian matrix of a connected weighted graph the equality cases for the bounds for spectral radii or least eigenvalues are also examined

block matrix generalizations of schur s basic theorems on hadamard products abstract in a classic 1911 paper i schur gave several useful bounds for the spectral norm and eigenvalues of the hadamard entrywise product of two matrices motivated by applications to the theory of monotone and convex matrix functions we are led to consider hadamard products in which both factors are conformally partitioned block matrices and the entries of one factor are constant within each block such products are special cases of a block kronecker tensor product and it is in this context that we present generalizations of schur s results

allowable spectral perturbations of zme matrices a zme matrix is a matrix a all of whose positive integer powers are z matrices and whose odd powers are irreducible we find a combinatorial partial order on the spectral idempotents of a zme matrix a which determines the allowable spectral perturbations b for which b is again a zme matrix we apply this result to show that under certain restrictions the product of two zme matrices is a zme matrix

description of the sub markov kernel associated to generalized ultrametric matrices an algorithmic approach abstract we supply a simple algorithm which describes the sub markov kernel p associated to a nonsingular generalized ultrametric matrix u this algorithm is based on the dyadic tree structure of u it identifies the exiting roots of p and p t and the couples i j for which p ij 0 equivalently u 1 ij

a classification of matrices of class z abstract we generalize the classes n 0 and f 0 studied by k fan g johnson and r smith schur complements and lattices are examined for matrices in these classes

fast wavelet transforms and numerical algorithms i a class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices in contrast the methods presented here are based on the recently developed theory of wavelets and are applicable to all calderon zygmund and pseudo differential operators the algorithms of this paper require order o n or o n log n operations to apply an n n matrix to a vector depending on the particular operator and the version of the algorithm being used and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here

inverse m matrix inequalities and generalized ultrametric matrices abstract we use weighted directed graphs to introduce a class of nonnegative matrices which under a simple condition are inverse m matrices we call our class the generalized ultrametic matrices since it contains the class of symmetric ultrametric matrices and some unsymmetric matrices we show that a generalized ultrametric matrix is the inverse of a row and column diagonally dominant m matrix if and only if it contains no zero row and no two of its rows are identical this theorem generalizes the known result that a symmetric strictly ultrametric matrix is the inverse of a strictly diagonally dominant m matrix we also present inequalities and conditions for equality among the entries of the inverse of a row diagonally dominant m matrix some of these inequalities and conditions for equality generalize results of stieltjes on inverses of symmetric diagonally dominant m matrices

on the hadamard product of inverse m matrices abstract we investigate the hadamard product of inverse m matrices and present two classes of inverse m matrices that are closed under the hadamard multiplication in the end we give some inequalities on the fan product of m matrices and schur complements

z matrices and inverse z matrices abstract we consider z matrices and inverse z matrices i e those nonsingular matrices whose inverses are z matrices recently fiedler and markham introduced a classification of z matrices this classification directly leads to a classification of inverse z matrices among all classes of z matrices and inverse z matrices the classes of m matrices n 0 matrices f 0 matrices and inverse m matrices inverse n 0 matrices and inverse f 0 matrices respectively have been studied in detail here we discuss each single class of z matrices and inverse z matrices as well as considering the whole classes of z matrices and inverse z matrices we establish some common properties of the classes such as eigenvalue bounds and determinant inequalities and we give a new characterization of some classes of z matrices and inverse z matrices moreover we prove that other classes besides those of m matrices n 0 matrices and f 0 matrices consist of matrices whose determinants have the same sign some of the results generalize known results for m matrices n 0 matrices and f 0 matrices and for inverse m matrices inverse n 0 matrices and inverse f 0 matrices however we also show that some properties of the specific classes mentioned above do not hold for all classes of z matrices and inverse z matrices

geometric aspects of the symmetric inverse m matrix problem abstract we investigate the symmetric inverse m matrix problem from a geometric perspective the central question in this geometric context is which conditions on the k dimensional facets of an n simplex s guarantee that s has no obtuse dihedral angles the simplest of such conditions is that if all triangular facets of s are equilateral then s is regular and thus nonobtuse first we study the properties of an n simplex s whose k facets are all nonobtuse and generalize some classical results by fiedler 14 we prove that if all n 1 facets of an n simplex s are nonobtuse each makes at most one obtuse dihedral angle with another facet this helps to identify a special type of tetrahedron which we will call sub orthocentric with the property that if all tetrahedral facets of s are sub orthocentric then s is nonobtuse rephrased in the language of linear algebra this constitutes a purely geometric proof of the fact that each symmetric ultrametric matrix 28 is the inverse of a weakly diagonally dominant m matrix the geometric proof provides valuable insights that supplement the discrete measure theoretic 24 and the linear algebraic 25 proof the review papers 20 21 support our believe that the linear algebraic perspective on the inverse m matrix problem dominates the literature the geometric perspective however connects sign properties of entries of inverses of a symmetric positive definite matrix to the dihedral angle properties of an underlying simplex and enables an explicit visualization of how these angles and signs can be manipulated this will serve to formulate purely geometric conditions on the k facets of an n simplex s that may render s nonobtuse also for k 3 for this we generalize the class of sub orthocentric tetrahedra that gives rise to the class of ultrametric matrices to sub orthocentric simplices that define symmetric positive definite matrices a with special types of k k principal submatrices for k 3 each sub orthocentric simplices is nonobtuse and we conjecture that any simplex with sub orthocentric facets only is sub orthocentric itself along the way several additional new concepts will be introduced such as vertex gramians simplicial matrix classes the dual hull and the sub orthocentric set of a nonobtuse simplex and nonblocking matrices these concepts may also be of use in a different linear algebraic setting in particular in the context if completely positive matrices for which we will prove some auxiliary results as well

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

new perturbation iteration solutions for bratu type equations perturbation iteration theory is systematically generated for both linear and nonlinear second order differential equations and applied to bratu type equations different perturbation iteration algorithms depending upon the number of taylor expansion terms are proposed using the iteration formulas derived using different perturbation iteration algorithms new solutions of bratu type equations are obtained solutions constructed using different perturbation iteration algorithms are contrasted with each other as well as with numerical solutions it is found that algorithms with more taylor series expansion terms yield more accurate results

inverse m matrices abstract this is an attempt at a comprehensive expository study of those nonnegative matrices which happen to be inverses of m matrices and is aimed at an audience conversant with basic ideas of matrix theory a theme is the parallels anddifferences between the class of m matrices and the class of inverse m matrices among the primary tools used are diagonal multiplications the neumann expansion and the form of the inverse of a partitioned matrix some of the results seem not to have appeared before and several unsolved problems are mentioned

double soules pairs and matching soules bases abstract we consider two generalizations of the notion of a soules basis matrix a pair of nonsingular n n matrices p q is called a double soules pair if the first columns of p and q are positive pq t i and p q t is nonnegative for every n n nonnegative diagonal matrix with nonincreasing diagonal elements in a paper by chen han and neumann an algorithm for generating such pairs was given here we characterize all such pairs and discuss some implications of the characterization we also consider pairs of matrices u v such that u and v each consists of k orthonormal columns the first of which is positive and u v is nonnegative for every k k nonnegative diagonal matrix with nonincreasing diagonal elements we call such pairs matching soules pairs we characterize all such pairs and make some observations regarding the nonnegative matrices and generalized inverses generated by them

the solutions to an infinite family of matrix inequalities involving zme matrices solutions for a certain infinite system of matrix inequalities are determined in these inequalities the coefficient matrices are zme matrices which were introduced by friedland hershkowitz and schneider the solutions are shown to have a simple form under certain restrictions on the magnitudes of the minimal eigenvalues of the coefficient matrices finally solutions to the system of inequalities are used to study the structure of reducible zm matrices

bounds on the spectrum of nonnegative matrices and certain z matrices spectral bounds are obtained for a type of z matrix using perron frobenius theory on the inverse these lead to spectral bounds for nonnegative matrices and m matrices these results are then extended using the result of rothblum and tan concerning the coefficient of ergodicity of a nonnegative matrix

on relationships between several classes of z matrices m matrices and nonnegative matrices abstract in this paper we establish relationships between several classes of well known matrices and some new classes of matrices we consider matrices whose powers are irreducible z matrices or m matrices these matrices are called zma matrices or mma matrices we establish a relationship between theses classe of matrices and the class of soules matrices moreover we prove that symmetric zma matrices and mma matrices are diagonally congruent to matrices that we call z sums and m sums conversely z sums and m sums are diagonally congruent to zma matrices and mma matrices this relationship exploits the structure of zma matrices and mma matrices and several well known properties of zma matrices follow immediately z sums and m sums are closely related to strictly ultrametric matrices sums we also characterize inverse zma matrices we prove that symmetric inverse zma matrices are diagonally congruent to shifted sums and that shifted sums are diagonally congruent to symmetric inverse zma matrices

splitting methods for the numerical approximation of some models of age structured population dynamics and epidemiology splitting methods for nonlinear models arising from population dynamics and epidemiology are described and analyzed a backward finite differencing along the characteristic is used for the approximation it is shown that the schemes are convergent at first order rate in the maximum norm the stability of the methods is discussed several numerical examples are presented

a characterization of the closure of inverse m matrices we give the explicit form of a matrix a to belong to m 1 the closure of inverse m matrices this completes a result from a previous paper of the authors and c r johnson and answers a question which was raised there to characterize singular matrices m 1

some connections between the drazin inverse p matrices and the closure of inverse m matrices abstract using results of a previous paper on the closure of inverse m matrices we find the drazin inverse of a matrix belonging to this closure in addition the structure of nonzero entries of the powers a 2 a 3 of such a matrix a is shown to be invariant and a result on p matrices is applied to matrices of this closure

some results on structured m matrices with an application to wireless communications in this paper we study conditions under which a specially structured z matrix is an m matrix we apply the result to a capacity problem in wireless communications

iterative differential quadrature solutions for bratu problem abstract a numerical scheme based on differential quadrature methods is introduced for solving bratu problem the problem is firstly reduced to an iterative one then both of differential quadrature method dqm and moving least squares differential quadrature method mlsdqm are applied to solve iteratively the nonlinear problem the proposed scheme successfully computes multiple solutions to bratu s problem the obtained results agree with the 1d and 2d closed forms further a parametric study is introduced to investigate the computational characteristics of the proposed scheme

on the spectrum of n0 matrices abstract the author studies the spectrum of n 0 matrices i e matrices of the form a i b where b 0 and 0 b here 0 is the maximum of the spectral radii of all principal submatrices of b of order n 1

modified chebyshev wavelet methods for fractional delay type equations in this article we develop the chebyshev wavelet method for solving the fractional delay differential equations and integro differential equations according to the development we approximate the delay unknown functions by the chebyshev wavelets series at delay time which we call the delay chebyshev wavelet series we also proposed a technique by combining the method of steps and chebyshev wavelet method for solving fractional delay differential equations this technique converts the fractional delay differential equation on a given interval to a fractional non delay differential equation over that interval by using the function defined on previous interval and then apply the chebyshev wavelet method on the obtained fractional non delay differential equation to find the solution numerical examples will be presented to demonstrate the benefits of computing with these approaches

inverse m matrix a new characterization abstract in this article we present a new characterization of inverse m matrices inverse row diagonally dominant m matrices and inverse row and column diagonally dominant m matrices based on the positivity of certain inner products

analytical study of fractional bratu type equation arising in electro spun organic nanofibers elaboration abstract in this article we present a hybrid analytical scheme namely homotopy perturbation transform method to achieve the solutions of the non linear bratu type problem with fractional order derivatives the caputo type fractional derivatives are considered in the present article he s polynomial is used to tackle the nonlinearity which arise in our considered problem using the initial conditions the numerical solutions of the problem are computed the numerical procedure reveals that only a few iterations are needed for better approximation of the solutions which illustrates the effectiveness and reliability of the method effects of fractional order derivatives on the solutions for various particular cases are depicted through graphs

characterization of symmetric m matrices as resistive inverses abstract we aim here at characterizing those nonnegative matrices whose inverse is an irreducible stieltjes matrix specifically we prove that any irreducible stieltjes matrix is a resistive inverse to do this we consider the network defined by the off diagonal entries of the matrix and we identify the matrix with a positive definite schrodinger operator whose ground state is determined by the lowest eigenvalue of the matrix and the corresponding positive eigenvector we also analyze the case in which the operator is positive semidefinite which corresponds to the study of singular irreducible symmetric m matrices

dynamics of the solution of bratu s equation abstract in the present report we examine the dynamics exhibited by the solution of bratu s equation it represents a one dimensional map with control parameter for certain values of the parameter it exhibits successive bifurcations and shows chaotic regimes this behaviour was confirmed by calculating the corresponding lyapunov exponent power spectra and cobweb diagrams indicating similarities with other well known one dimensional maps

notes on f0 matrices abstract the author studies f 0 matrices and shows that n n matrix a f 0 if and only if a ti b with b 0 and n 2 b t n 1 b where k b denotes the maximum of the spectral radii of all k principal submatrices of b also an inverse f 0 matrix problem is considered