a fast and accurate algorithm for solving bernstein vandermonde linear systems abstract a fast and accurate algorithm for solving a bernstein vandermonde linear system is presented the algorithm is derived by using results related to the bidiagonal decomposition of the inverse of a totally positive matrix by means of neville elimination the use of explicit expressions for the determinants involved in the process serves to make the algorithm both fast and accurate

a study of the performance of neville elimination using two kinds of partitioning techniques abstract in this paper a method to compute the solution of a system of linear equations by means of neville elimination is described using two kinds of partitioning techniques block and block striped this type of approach is especially suited to the case of totally positive linear systems which is present in different fields of application although neville elimination carried out more floating point operations than gaussian elimination in some cases in this study we confirm that these advantages disappear when we use multiprocessor systems on the other hand the overall parallel run time of neville elimination is better than gauss time as neville elimination uses a lower cost communication model

a criterion for stability of matrices a necessary and sufficient condition for the stability ofn nmatrices with real entries is proved applications to asymptotic stability of equilibria for vector fields are considered the results offer an alternative to the well known routh hurwitz conditions

the iterative solution of the matrix equation xa bx c 0 abstract an iterative procedure is presented for the solution of the matrix equation xa bx c 0 for complex matrices a b and c known iterative solution techniques converging when a and b are stable follow as special cases of this general formulation

hermite biehler routh hurwitz and total positivity simple proofs of the hermite biehler and routh hurwitz theorems are presented the total nonnegativity of the hurwitz matrix of a stable real polynomial follows as an immediate corollary

positive symmetric matrices with exactly one positive eigenvalue abstract several properties of positive symmetric matrices with exactly one positive eigenvalue are analyzed they include their ldl t factorization as well as the growth factor of symmetric pivoting strategies applied to these matrices an efficient test to check if a given positive symmetric matrix has exactly one positive eigenvalue is presented the relationship with other classes of matrices is analyzed

full rank factorization in echelon form of totally nonpositive negative rectangular matrices abstract an n m real matrix a is said to be totally nonpositive negative if every minor is nonpositive negative in this paper we study the full rank factorization in echelon form of a totally nonpositive negative matrix this characterization allows us to significantly reduce the number of minors to be checked in order to decide the total negativity of a matrix

decompositions of strictly sign regular matrices abstract a matrix is called strictly sign regular if for each k all its k k minors are nonzero and have the same sign we study several decompositions of strictly sign regular matrices including qr decomposition schur decomposition svd and symmetric triangular decomposition several characterizations are provided

neville elimination for rank structured matrices abstract in this paper it is shown that neville elimination is suited to exploit the rank structure of an order r quasiseparable matrix a c n n by providing a condensed decomposition of a as product of unit bidiagonal matrices all together specified by o nr parameters at the cost of o nr 3 flops an application of this result for eigenvalue computation of totally positive rank structured matrices is also presented

eigenvalue generalized eigenvector assignment by output feedback this note generalizes the previous results of the closed loop eigenstructure assignment via output feedback in linear multivariable systems necessary and sufficient conditions for the closed loop eigenstructure assignment by output feedback are presented some known results on entire eigenstructure assignment are deduced from this result

a conceptual model of the soil water retention curve a conceptual model based on the assumption that soil structure evolves from a uniform random fragmentation process is proposed to define the water retention function the fragmentation process determines the particle size distribution of the soil the transformation of particles volumes into pore volumes via a power function and the adoption of the capillarity equation lead to an expression for the water retention curve this expression presents two fitting parameters only the proposed model is tested on water retention data sets of 12 soils representing a wide range of soil textures from sand to clay the agreement between the fitted curves and the measured data is very good the performances of the model are also compared with those of the two parameter models of van genuchten 1980 and russo 1988 for the water retention function in general the proposed model exhibits increased flexibility and improves the fit at both the high and the low water contents range

linear operators preserving certain equivalence relations originating in system theory abstract let f be c or r a finite dimensional linear time invariant system is described in state space form by xdot ax bu y cx du and is identified with the matrix 4 tuple a b c d where x f n u f m y f p and a b c d are matrices of appropriate sizes and with entries in f for fixed n m p let m be the linear space of all systems a b c d equivalence relations can be defined on m based on the possibility of changes of basis inthe state space the input space or the output space and the possibility of state feedback and or output feedback we characterize those nonsingular linear operators on m that satisfy x y whenever x y

the solution of the equation xa axt 0 and its application to the theory of orbits abstract describe how to find the general solution of the matrix equation xa ax t 0 with a c n n which allows us to determine the dimension of its solution space this result has immediate applications in the theory of congruence orbits of matrices in c n n because the set xa ax t x c n n is the tangent space at a to the congruence orbit of a hence the codimension of this orbit is precisely the dimension of the solution space of xa ax t 0 as a consequence we also determine the generic canonical structure of matrices under the action of congruence all these results can be directly extended to palindromic pencils a a t

characterizations and stable tests for the routh hurwitz conditions and for total positivity given a polynomial of degree n a test of o n2 elementary operations and growth factor 1 is presented in order to check the routh hurwitz conditions this optimal growth factor guarantees that the test presents better stability properties than other known tests we also present a test of o n3 elementary operations and growth factor 1 in order to check if a matrix is strictly totally positive finally totally positive matrices are characterized by their symmetric triangular decompositions

corner cutting algorithms for the bezier representation of free form curves abstract we give a general treatment of the problem of converting a curve expressed in a b spline expansion into its bezier form we show that corner cutting of the b spline control polygon leads to the bezier points exactly when the bezier matrix is totally positive also for spline spaces used to model space curves with curvature continuity we give an algorithm for determining the bezier representation

explicit factorization of the vandermonde matrix the lu factorization of the vandermonde matrix is obtained using complete symmetric functions and the lower and upper triangular matrices are in turn factorized into 1 banded matrices thus expressing the vandermonde matrix as a product of 1 banded matrices

gradient based iterative solutions for general linear matrix equations in this paper we present a gradient based iterative algorithm for solving general linear matrix equations by extending the jacobi iteration and by applying the hierarchical identification principle convergence analysis indicates that the iterative solutions always converge fast to the exact solutions for any initial values and small condition numbers of the associated matrices two numerical examples are provided to show that the proposed algorithm is effective

fast and accurate algorithms for jacobi stirling matrices abstract jacobi stirling numbers of first and second kind and their corresponding associated matrices play an important role in combinatorics this paper presents an efficient method that guarantees that the computation of the singular values and the inverses of these matrices can be performed with high relative accuracy numerical examples are included

growth factors of pivoting strategies associated with neville elimination neville elimination is a direct method for solving linear systems several pivoting strategies for neville elimination including pairwise pivoting are analyzed bounds for two different kinds of growth factors are provided finally an approximation of the average normalized growth factor associated with several pivoting strategies is computed and analyzed using random matrices

models of the water retention curve for soils with a fractal pore size distribution the relationship between water content and water potential for a soil is termed its water retention curve this basic hydraulic property is closely related to the soil pore size distribution for which it serves as a conventional method of measurement in this paper a general model of the water retention curve is derived for soils whose pore size distribution is fractal in the sense of the mandelbrot number size distribution this model which contains two adjustable parameters the fractal dimension and the upper limiting value of the fractal porosity is shown to include other fractal approaches to the water retention curve as special cases application of the general model to a number of published data sets covering a broad range of soil texture indicated that unique independent values of the two adjustable parameters may be difficult to obtain by statistical analysis of water retention data for a given soil discrimination among different fractal approaches thus will require water retention data of high density and precision

closed form solutions to the nonhomogeneous yakubovich conjugate matrix equation some closed form solutions are provided for the nonhomogeneous yakubovich conjugate matrix equation email protected f by r with x and y being unknown matrices the presented solutions can offer all the degrees of freedom which is represented by an arbitrarily chosen parameter matrix the primary feature of the solutions is that the matrices f and r are not restricted to be in any canonical form or may be even unknown a priori one of the solutions is neatly expressed in terms of controllability matrices and observability matrices

accurate computations with collocation matrices of rational bases the rational bernstein basis plays a crucial role in computer aided geometric design the collocation matrices of this basis are called rational bernstein vandermonde matrices in this paper we provide algorithms for computing the bidiagonal decomposition of rational bernstein vandermonde matrices and their inverses with high relative accuracy similar results are obtained for the collocation matrices of another important rational basis the rational said ball basis it is also shown that these algorithms can be used to perform accurately some computations with these matrices such us the calculation of their inverses their eigenvalues or their singular values numerical experiments illustrate the results

accurate bidiagonal decomposition of totally positive cauchy vandermonde matrices and applications abstract cauchy vandermonde matrices play a fundamental role in rational interpolation theory and in other fields when all their corresponding nodes are different and positive and all poles are different and negative and follow adequate orderings these matrices are totally positive in this paper we provide fast algorithms for computing bidiagonal factorizations of these matrices and their inverses with high relative accuracy these algorithms can be used to solve with high relative accuracy other algebraic problems such as the computation of all singular values all eigenvalues or the solution of certain linear systems the error analysis of the algorithm for computing the bidiagonal factorization and the corresponding perturbation theory are also performed

closed form solutions to the nonhomogeneous yakubovich transpose matrix equation abstract the nonhomogeneous yakubovich transpose matrix equation x a x t b c y r which contains the well known kalman yakubovich transpose matrix equation and general discrete lyapunov transpose matrix equation as special cases has many important applications in control system theory this study presents two methods to obtain the closed form solutions of the nonhomogeneous yakubovich transpose matrix equation moreover the equivalent forms of the solutions are provided and one of the solutions is established with the controllability matrix the observability matrix and symmetric operator matrix

accurate bidiagonal decomposition of totally positive h bernstein vandermonde matrices and applications abstract an algorithm for the computation of the bidiagonal decomposition of strictly totally positive h bernstein vandermonde matrices is presented these matrices are collocation matrices of h bernstein bases a generalization of the bernstein basis of the space of polynomials of degree less than or equal to n the algorithm is fast its computational complexity is o n 2 and has high relative accuracy the computation of this bidiagonal decomposition is used as the initial stage for the accurate and efficient solution of several linear algebra problems with these matrices linear system solving eigenvalue computation and inverse computation numerical experiments are also included

iterative algorithms for solving the matrix equation axb cx td e in this paper we propose two iterative algorithms to solve the matrix equation axb cx td e the first algorithm is applied when the matrix equation is consistent in this case for any special initial matrix x 1 a solution the minimal frobenius norm solution can be obtained within finite iteration steps in the absence of roundoff errors the second algorithm is applied when the matrix equation is inconsistent in this case for any special initial matrix x 1 a least squares solution the minimal frobenius norm least squares solution can be obtained within finite iteration steps in the absence of roundoff errors some examples verify the efficiency of these algorithms

total positivity and the qr algorithm abstract an n n real matrix a is tp totally positive if all its minors are positive or zero ntp if it is nonsingular and tp stp if it is strictly tp o oscillatory if it is tp and a power a m is stp let p be one of ntp o stp we prove that if a is symmetric and has property p is not an eigenvalue of a and a i qr and a i rq with r having positive diagonal then a has property p and vice versa the analysis includes a new criterion for a to be stp

a stable test for strict sign regularity a stable test to check if a given matrix is strictly sign regular is provided among other nice properties we prove that it has an optimal growth factor the test is compared with other alternative tests appearing in the literature and its advantages are shown

elimination technique from extrapolation to totally positive matrices and cagd in this survey we will show some connections between several mathematical problems such as extrapolation linear systems totally positive matrices and computer aided geometric design with elimination techniques as the common tool to deal with all of them

factorizations of cauchy vandermonde matrices abstract this paper analyzes the factorization of the inverse of a cauchy vandermonde matrix as a product of bidiagonal matrices factorizations of cauchy vandermonde matrices are also considered the results are applied to derive a fast algorithm for solving linear systems whose coefficient matrices are cauchy vandermonde matrices

technical communique complete parametric approach for eigenstructure assignment in a class of second order linear systems this note deals with eigenstructure assignment in the second order linear system email protected email protected cq bu using the proportional plus derivative feedback controller u k 0q k email protected under the controllability condition of the matrix pair ab very simple general and complete parametric expressions in direct closed forms for both the closed loop eigenvector matrix and the feedback gains are established in terms of the closed loop eigenvalues and a group of parameter vectors the main computations are two sets of elementary matrix transformations which can be replaced by a series of singular value decompositions when the closed loop eigenvalues are chosen a priori the approach utilizes directly the original system data a b and c and involves manipulations on only n dimensional matrices an example illustrates the effect of the proposed approach

on the schur and singular value decompositions of oscillatory matrices abstract a square matrix a is said to be oscillatory if it has nonnegative minors and some power ak of a is strictly totally positive i e ak has strictly positive minors we study the schur and singular value decompositions of oscillatory matrices some applications are provided

accurate computations with said ball vandermonde matrices abstract a generalization of the vandermonde matrices which arise when the power basis is replaced by the said ball basis is considered when the nodes are inside the interval 0 1 then those matrices are strictly totally positive an algorithm for computing the bidiagonal decomposition of those said ball vandermonde matrices is presented which allows us to use known algorithms for totally positive matrices represented by their bidiagonal decomposition the algorithm is shown to be fast and to guarantee high relative accuracy some numerical experiments which illustrate the good behaviour of the algorithm are included

a test and bidiagonal factorization for certain sign regular matrices abstract it is well known that a totally nonnegative matrix can be characterized in terms of its bidiagonal factorization which is critical to perform accurate computations however there is no known such factorization of other sign regular matrices in this paper we provide a characterization and test for certain sign regular matrices with the same signature sequence as that of nonsingular jacobi sign regular matrices consequently a bidiagonal factorization is derived for such sign regular matrix which in turn provides an effective way to generate these sign regular matrices

toward solution of matrix equation x af x b c abstract this paper studies the solvability existence of unique solution closed form solution and numerical solution of matrix equation x af x b c with f x x t f x x and f x x h where x is the unknown it is proven that the solvability of these equations is equivalent to the solvability of some auxiliary standard stein equations in the form of w a w b c where the dimensions of the coefficient matrices a b and c are the same as those of the original equation closed form solutions of equation x af x b c can then be obtained by utilizing standard results on the standard stein equation on the other hand some generalized stein iterations and accelerated stein iterations are proposed to obtain numerical solutions of equation x af x b c necessary and sufficient conditions are established to guarantee the convergence of the iterations

a system of real quaternion matrix equations with applications abstract let h be the real quaternion algebra and h n m denote the set of all n m matrices over h let p h n n and q h m m be involutions i e p 2 i q 2 i a matrix a h n m is said to be p q symmetric if a paq this paper studies the system of linear real quaternion matrix equations a 1 x 1 c 1 x 1 b 1 c 2 a 2 x 2 c 3 x 2 b 2 c 4 a 3 x 1 b 3 a 4 x 2 b 4 c c we present some necessary and sufficient conditions for the existence of a solution to this system and give an expression of the general solution to the system when the solvability conditions are satisfied as applications we discuss the necessary and sufficient conditions for the system a a x c a xb b c b a c xb c c c to have a p q symmetric solution we also show an expression of the p q symmetric solution to the system when the solvability conditions are met moreover we provide an algorithm and a numerical example to illustrate our results the findings of this paper extend some known results in the literature

total positivity and neville elimination abstract neville elimination is described in terms of schur complements of matrices and used to improve some well known characterizations of totally positive and strictly totally positive matrices

the re nonnegative definite and re positive definite solutions to the matrix equation axb d in this paper the re nonnegative definite re nnd and re positive definite re pd solutions of the matrix equation axb d are considered the necessary and sufficient conditions for the existence of re nnd and re pd solutions to the equation are provided and the explicit representations of the general re nnd and re pd solutions are given when it is solvable

accurate computations with lupa matrices lupa q analogues of the bernstein functions play an important role in approximation theory and computer aided geometric design their collocation matrices are called lupa matrices in this paper we provide algorithms for computing the bidiagonal decomposition of these matrices and their inverses to high relative accuracy it is also shown that these algorithms can be used to perform to high relative accuracy several algebraic calculations with these matrices such as the calculation of their inverses their eigenvalues or their singular values numerical experiments are included

on nonsingular sign regular matrices abstract an m n matrix a is sign regular if for each k 1 k min m n all k k submatrices of a have determinant with the same nonstrict sign the zero pattern of nonsingular sign regular matrices is analyzed it is proved that the number of zero entries which can appear in a nonsingular sign regular matrix depends on its signature a matrix is totally nonpositive if all its minors are nonpositive a test for recognizing nonsingular totally nonpositive matrices is also provided

rank structure properties of rectangular matrices admitting bidiagonal type factorizations abstract in this paper we investigate the class of rectangular matrices that admit bidiagonal type factorizations by neville elimination without exchanges we provide a complete characterization for a rectangular matrix to be factored as a product of bidiagonal factors and a banded factor in terms of rank structure properties consequently we give a complete characterization of the class of rectangular matrices that have neville factorizations

on the boundary of totally positive upper triangular matrices abstract let b gl n r denote the subgroup of upper triangular n n matrices with positive entries on the main diagonal a matrix m b is called totally positive if the determinants of all its minors not containing a row or column lying completely under the main diagonal are positive we give a simple determinantal equation for the boundary of all positive upper triangular matrices in b

bidiagonal decompositions of oscillating systems of vectors abstract we establish necessary and sufficient conditions in the language of bidiagonal decompositions for a matrix v to be an eigenvector matrix of a totally positive matrix namely this is the case if and only if v and v t are lowerly totally positive these conditions translate into easy positivity requirements on the parameters in the bidiagonal decompositions of v and v t using these decompositions we give elementary proofs of the oscillating properties of v in particular the fact that the jth column of v has j 1 changes of sign our new results include the fact that the q matrix in a qr decomposition of a totally positive matrix belongs to the above class and thus has the same oscillating properties

full rank factorization in quasi ldu form of totally nonpositive rectangular matrices abstract let a a i j r n m be a totally nonpositive matrix with rank a r min n m and a 11 0 in this paper we obtain a characterization in terms of the full rank factorization in quasi ldu form that is a l d u where l r n r is a block lower echelon matrix u r r m is a unit upper echelon totally positive matrix and d r r r is a diagonal matrix with rank l rank u rank d r we use this quasi ldu decomposition to construct the quasi bidiagonal factorization of a moreover some properties about these matrices are studied

new approach to robust observer design this paper shows that based on the recent development of observer design solution an observer pole selection method can be formulated to minimize the observer gain to the system input it is proved that this method is a deterministic approach to the recovery of the loop transfer function and robustness of direct state feedback systems

the approximation of a totally positive band matrix by a strictly banded totally positive one every nonsingular totally positive m banded matrix is shown to be the product of m totally positive one banded matrices and therefore the limit of strictly m banded totally positive matrices this result is then extended to bi infinite m banded totally positive matrices with linearly independent rows and columns in the process such matrices are shown to possess at least one diagonal whose principal sections are all nonzero as a consequence such matrices are seen to be approximable by strictly m banded totally positive ones

determinantal criteria for total positivity a matrix is totally positive respectively strictly totally positive if all its minors are nonnegative respectively positive in this paper we revisit the main determinantal criteria for these matrices and provide two new ones one of them for the total positivity of m n matrices with any n consecutive rows linearly independent and another one to check if an n n totally positive matrix has all minors of order less than k k n positive

gradient based and least squares based iterative algorithms for matrix equations axb cxtd f abstract this paper develops a gradient based and a least squares based iterative algorithms for solving matrix equation axb cx t d f the basic idea is to decompose the matrix equation system under consideration into two subsystems by applying the hierarchical identification principle and to derive the iterative algorithms by extending the iterative methods for solving ax b and axb f the analysis shows that when the matrix equation has a unique solution under the sense of least squares the iterative solution converges to the exact solution for any initial values a numerical example verifies the proposed theorems

bernstein bezoutian matrices and curve implicitization a new application of bernstein bezoutian matrices a type of resultant matrices constructed when the polynomials are given in the bernstein basis is presented in particular the approach to curve implicitization through sylvester and bezout resultant matrices and bivariate interpolation in the usual power basis is extended to the case in which the polynomials appearing in the rational parametric equations of the curve are expressed in the bernstein basis avoiding the basis conversion from the bernstein to the power basis the coefficients of the implicit equation are computed in the bivariate tensor product bernstein basis and their computation involves the bidiagonal factorization of the inverses of certain totally positive matrices

polynomial least squares fitting in the bernstein basis the problem of polynomial least squares fitting in which the usual monomial basis is replaced by the bernstein basis is considered the coefficient matrix of the overdetermined system to be solved in the least squares sense is then a rectangular bernstein vandermonde matrix in order to use the method based on the qr decomposition of a the first stage consists of computing the bidiagonal decomposition of the coefficient matrix a starting from that bidiagonal decomposition an algorithm for obtaining the qr decomposition of a is the applied finally a triangular system is solved by using the bidiagonal decomposition of the r factor of a some numerical experiments showing the behavior of this approach are included

a test for strict sign regularity a characterization of strict sign regular matrices is obtained it is given in an algorithmic form which allows the easy construction of a test to check if a matrix is strictly sign regular the test is based on the neville elimination of several submatrices of a and requires less computational work than those which can be derived from other previously known characterizations of these matrices

three parameter lognormal distribution model for soil water retention many models for soil water retention have been proposed however most of these models are curve fitting equations and do not emphasize the physical significance of their empirical parameters a new retention model that exhibits increased flexibility was developed by applying three parameter lognormal distribution laws to the pore radius distribution function r and to the water capacity function which was taken to be the pore capillary pressure distribution function this model contains three parameters that are closely related to the statistics of the bubbling pressure c the mode 0 of and the standard deviation of transformed by comparison of this model with three existing models the van genuchten model the brooks corey model and the modified tani model it was shown that c 0 and are all essential for a general retention model

spectral properties of sums of certain kronecker products we introduce two kinds of sums of kronecker products and their induced operators we study the algebraic properties of these two kinds of matrices and their associated operators the properties include their eigenvalues their eigenvectors and the relationships between their spectral radii or spectral abscissae furthermore two projected matrices of these kronecker products and their induced operators are also studied

statistical evaluation and choice of soil water retention models 1 this paper presents the results of statistical investigations for the evaluation of soil water retention models swrms we employed three different methods developed for model selection in the field of nonlinear regression namely simulation studies analysis of nonlinearity measures and resampling strategies such as cross validation and bootstrap methods using these methods together with small data sets we evaluated the performance of three exemplarily chosen types of swrms with respect to their parameter properties and the reliability of model predictions the resulting rankings of models show that the favorable models are characterized by few parameters with an almost linear estimation behavior and close to symmetric distributions to further demonstrate the potential of the statistical methods in the field of model selection a modification of the four parameter van genuchten model is proposed which shows significantly improved and robust statistical properties

analyses of infiltration events in relation to determining soil hydraulic properties by inverse problem methodology at the field scale because of the relatively large number of observation points required to estimate the spatial distributions of hydraulic properties application of inversion procedures must be based on a characteristic of the flow that for a given point in the field can be measured with relative ease and can be used as input for the inversion procedure suggesting the use of infiltration data for this purpose and recognizing the fact that a basic requirement for the design of a transient flow experiment is that the resulting inverse problem be sufficiently well posed to allow solution this paper addresses the question under which circumstances the resulting inverse problem is well posed utilizing the concepts of identifiability uniqueness and stability for this purpose three different models of the soil hydraulic properties were analyzed the main conclusion of this study is that when infiltration data measured at the darcy scale are used as input for the inversion procedure the inclusion of prior information on a single measurable parameter the saturated conductivity ks in the estimation criterion will enhance the likelihood of uniqueness and stability of the inverse solution provided that the structure of the hydraulic model is sufficiently simple however since for a particular situation it is impossible to determine a priori whether the resultant inverse problem is well posed or not this must be carried out only a posteriori by solving the problem several times with different initial parameter estimates accompanied by an analysis of the associated estimation errors

determining soil hydraulic properties by parameter estimation on the selection of a model for the hydraulic properties parameter estimation procedures involving solution of the inverse flow problem pertinent to a transient experiment constitute a powerful method of determining the soil hydraulic properties one of the problems associated with these procedures is the selection of an appropriate model to describe the soil hydraulic properties three different models were considered those of van genuchten vg and brooks and corey bc model and the exponential model of gardner for the hydraulic conductivity soil water pressure relationships coupled with a new expression for the soil water content soil water pressure relationship gr model for a given model the soil hydraulic properties were determined from simulated and measured outflow experiments supplemented with water content at a soil water pressure head of 15 000 cm h2o using the parameter estimation procedure of kool et al 1985a and data from two soils a hypothetical sandy loam soil assumed to be described by the vg model and a silt loam soil model validation tests were performed and the most appropriate model was selected from the candidate models by discrimination tests using the akaike information criterion aic in the case of the hypothetical sandy loam the vg model was found to be the most accurate and most consistent with the data the performance of both the bc and the gr models in terms of the aic was less good but very similar to each other in the case of the silt loam soil the vg model with additional parameter m which accounts for the correlation between pores and for the flow path tortuosity m 2 02 rather than a constant m 0 5 was found to be most accurate and most consistent with the data the performance of the bc and the gr models was similar when m was considered as an unknown parameter instead of a constant

accurate computation of the moore penrose inverse of strictly totally positive matrices abstract the computation of the moore penrose inverse of structured strictly totally positive matrices is addressed since these matrices are usually very ill conditioned standard algorithms fail to provide accurate results an algorithm based on the q r factorization and which takes advantage of the special structure and the totally positive character of these matrices is presented the first stage of the algorithm consists of the accurate computation of the bidiagonal decomposition of the matrix numerical experiments illustrating the good behavior of our approach are included

consecutive column and row properties of matrices and the loewner neville factorization abstract we say that a square matrix over a ring with identity has the consecutive column property if for all k all its relevant submatrices having k consecutive rows and the first k columns are invertible similarly the consecutive row cr is defined we show that analogously to the commutative case for totally positive matrices a matrix has both cc and cr properties if and only if it admits a certain loewner neville type factorization with invertible entries this factorization is unique since the result is proved for matrices in such generality it holds also for block matrices over a field with all blocks square explicit both ways formulae are found between two sets of parameters the loewner neville coefficients in the factorization and the schur complements of relevant submatrices in relevant submatrices larger by one we also show that for lower triangular matrices the cc property is preserved by inversion

a plu factorization of rectangular matrices by the neville elimination in this paper we prove that neville elimination can be matricially described by elementary matrices a plu factorization is obtained for any n m matrix where p is a permutation matrix l is a lower triangular matrix product of bidiagonal factors and u is an upper triangular matrix this result generalizes the neville factorization usually applied to characterize the totally positive matrices we prove that this elimination procedure is an alternative to gaussian elimination and sometimes provides a lower computational cost

further remarks on the cayley hamilton theorem and leverrier s method for the matrix pencil se a some results for matrix pencils are extended to the singular case se a a singular leverrier s relation cayley hamilton theorem and newton s formula are given a finite series expansion for se a 1 is given in terms of the generalized tschirnhausen polynomials

accurate solutions of product linear systems associated with rank structured matrices abstract in this paper we consider how to accurately solve linear systems associated with a wide class of rank structured matrices containing the well known vandermonde and cauchy matrices i e consecutive rank descending crd matrices we provide a mechanism to guarantee that the inverse of any product of crd matrices is generated in a subtraction free manner with the mechanism the solutions of linear systems associated with such products are accurately determined by the parameters of crd factors and we then accurately compute the solutions as warranted by these parameters in particular linear systems associated with products of vandermonde and cauchy matrices whose nodes satisfy certain positive or negative properties are solved to high relative accuracy error analysis and numerical experiments are provided to confirm the high accuracy

numerically robust pole assignment for second order systems we propose two new methods for solution of the eigenvalue assignment problem associated with the second order control system global hsize 30pc specifically the methods construct feedback matrices f 1 and f 2 such that the closed loop quadratic pencil has a desired set of eigenvalues and the associated eigenvectors are well conditioned method 1 is a modification of the singular value decomposition based method proposed by juang and maghami which is a second order adaptation of the well known robust eigenvalue assignment method by kautsky et al for first order systems method 2 is an extension of the recent non modal approach of datta and rincon for feedback stabilization of second order systems robustness to numerical round off errors is achieved by minimizing the condition numbers of the eigenvectors of the closed loop second order pencil control robustness to large plant uncertainty will not be explicitly considered in this paper numerical results for both the two methods are favourable a compara

an eigenstructure assignment algorithm for the design of fault detection filters in this paper we present an algorithm for the construction of detection spaces in a fault detection filter by direct eigenstructure assignment the algorithm permits great flexibility and simplifies the process of designing fault detection filters

componentwise backward error analysis of neville elimination abstract in this paper we perform a backward error analysis of neville elimination whenever there need row exchanges componentwise backward error bounds are presented for this elimination procedure applied to any nonsingular matrices consequently it is shown that neville elimination with two determinant pivoting proposed by cortes and pena 2007 5 is an excellent method for the triangularization of nonsingular sign regular matrices including totally nonnegative and totally nonpositive matrices which has a pleasantly small componentwise relative backward error in particular a small componentwise relative error bound is also provided for the bidiagonal factorization of totally nonnegative matrices

least squares solution with the minimum norm to general matrix equations via iteration two iterative algorithms are presented in this paper to solve the minimal norm least squares solution to a general linear matrix equations including the well known sylvester matrix equation and lyapunov matrix equation as special cases the first algorithm is based on the gradient based searching principle and the other one can be viewed as its dual form necessary and sufficient conditions for the step sizes in these two algorithms are proposed to guarantee the convergence of the algorithms for arbitrary initial conditions sufficient condition that is easy to compute is also given moreover two methods are proposed to choose the optimal step sizes such that the convergence speeds of the algorithms are maximized between these two methods the first one is to minimize the spectral radius of the iteration matrix and explicit expression for the optimal step size is obtained the second method is to minimize the square sum of the f norm of the error matrices produced by the algorithm and it is shown that the optimal step size exits uniquely and lies in an interval several numerical examples are given to illustrate the efficiency of the proposed approach

a collection of examples where neville elimination outperforms gaussian elimination neville elimination is an elimination procedure alternative to gaussian elimination it is very useful when dealing with totally positive matrices for which nice stability results are known here we include examples most of them test matrices used in matlab which are not totally positive matrices where neville elimination outperforms gaussian elimination

factorizations of confluent cauchy vandermonde matrices abstract the confluent cauchy vandermonde matrices are considered which were studied earlier by various authors in different way in this paper we analyze the factorization of the inverse of a special type of confluent cauchy vandermonde matrix as a product of block bidiagonal matrices by using block neville elimination factorizations of confluent cauchy vandermonde matrices are also considered which generalize the results of j j martinez j m pena factorizations of cauchy vandermonde matrices linear algebra appl 284 1998 229 237

neville elimination a study of the efficiency using checkerboard partitioning abstract it is well known that checkerboard partitioning can exploit more concurrency than striped partitioning because the matrix computation can be divided among more processors than in the case of striping in this work we analyze the performance of neville method when a checkerboard partitioning is used focusing on the special case of block cyclic checkerboard partitioning this method is an alternative to gaussian elimination and it has been proved to be very useful for some classes of matrices such as totally positive matrices the performance of this parallel system is measured in terms of the efficiency the fraction of time for which a processor is usefully employed which in our model is close to one when the optimum block size is used also we have executed our algorithms on a parallel pc cluster observing that both efficiencies theoretical and empirical are quite similar

a matricial description of neville elimination with applications to total positivity abstract the neville elimination process used by the authors in some previous papers in connection with totally positive matrices is studied in detail in the case of nonsingular matrices a wide class of matrices is found where neville elimination has a lower computational cost than gauss elimination finally some new characterizations are obtained for strictly totally positive and nonsingular totally positive matrices in terms of their neville elimination and that of their inverses

estimation of brooks corey parameters from water retention data the parameters of the brooks corey soil moisture characteristic may be determined by either graphical or automatic numerical procedures a popular log log procedure for automatic estimation leads to a linear least squares optimization problem apparently it has been applied incorrectly in the past when all measurements were used for parameter estimation and this realization explains the inconsistencies in some published data its proper application generally requires the solution of more than one linear problem for each data set alternatively a nonlinear procedure will yield parameter estimates directly in either case there may exist multiple local minima in the sum of squared deviations between model and measurements and the parameter estimates so derived are demonstrably unreliable this appears to be a result of the distinct air entry suction implicit in the brooks corey model and usually absent in field measured characteristic curves a new procedure based on an integral objective function overcomes the problems cited

bidiagonal decomposition of rectangular totally positive said ball vandermonde matrices error analysis perturbation theory and applications abstract an algorithm for computing the bidiagonal decomposition of said ball vandermonde matrices in the rectangular case is presented which allows one to use known algorithms for totally positive matrices represented by their bidiagonal decomposition the algorithm is fast and possesses high relative accuracy the error analysis of the algorithm is also addressed along with the perturbation theory for the bidiagonal factorization of totally positive said ball vandermonde matrices some numerical experiments showing the good behavior of the algorithm are included