structured total least squares and l2 approximation problems abstract it is shown how structured and weighted total least squares and l 2 approximation problems lead to a nonlinear generalized singular value decomposition an inverse iteration scheme to find a local minimum is proposed the emphasis of the paper is not on the convergence analysis of the algorithm rather the purpose is to illustrate its use in numerous applications in systems and control including total least squares with relative errors and or fixed elements inverse singular value problems an errors in variables variant of the kalman filter impulse response realization from noisy data h 2 model reduction h 2 system identification and calculating the largest stability radius of uncertain linear systems several numerical examples are given

spectral functions for real symmetric toeplitz matrices we derive separate spectral functions for the even and odd spectra of a real symmetric toeplitz matrix which are given by the roots of those functions these are rational functions also commonly referred to as secular functions two applications are considered spectral evolution as a function of one parameter and the computation of eigenvalues

construction of a hermitian toeplitz matrix from an arbitrary set of eigenvalues a solution to the inverse eigenvalue problem for hermitian toeplitz matrices is presented the approach taken is to first construct a real symmetric negacyclic matrix of order 2n and to then relate the negacyclic matrix to a hermitian toeplitz matrix of order n with the desired eigenspectrum

optimal domain splitting for interpolation by chebyshev polynomials polynomial interpolants defined using chebyshev extreme points as nodes converge uniformly at a geometric rate when sampling a function that is analytic on an interval however the convergence rate can be arbitrarily close to unity if the function has a singularity close to the interval when extended to the complex plane in such cases splitting the interval and doing piecewise interpolation may be more efficient in the total number of nodes than the global interpolant because the convergence rate is determined by bernstein ellipses obtained through a joukowski conformal map relative efficiency of splitting at any point in the interval can be calculated and then optimized over the interval the optimal splitting may be applied recursively the chebfun software project uses a simple rule of thumb without prior singularity information to create a binary search that can be shown to do an excellent job of finding the optimal splitting in most cases however the process can use a large number of intermedi

solving the inverse eigenvalue problem via the eigenvalue matrix abstract a numerical algorithm for the inverse eigenvalue problem for symmetric matrices is developed based on continually updating the eigenvector matrix using plane rotations a fundamental tool in the algorithm is a matrix formed from the rayleigh quotients of the eigenvectors with respect to each of the basis matrices involved with the basis orthonormalized with respect to the frobenius inner product two criteria of closeness to a solution are defined either of which makes it possible to monitor progress towards a solution the computational questions involved in this approach are examined in detail numerical examples are given for toeplitz and centrosymmetric tridiagonal matrices the new algorithm is much more robust than newton s method

continuous functions on totally ordered spaces that are compact in their order topologies abstract the totally ordered spaces that are compact and connected in their order topologies are characterized as images of lexicographic cubes the banach space of continuous functions on the lexicographic product of compact totally ordered spaces whose spaces of continuous functions have locally uniformly convex norms has an equivalent locally uniformly convex norm if and only if the product is countable the banach space of continuous functions on a compact totally ordered space always has an equivalent kadec norm those compact totally ordered spaces for which the banach space of continuous functions has an equivalent locally uniformly convex norm are characterized in terms of the bounded decreasing interval functions that can be defined on the intervals of the totally ordered spaces some examples are discussed in detail

on inverse eigenvalue problems for block toeplitz matrices with toeplitz blocks we propose an algorithm for solving the inverse eigenvalue problem for real symmetric block toeplitz matrices with symmetric toeplitz blocks it is based upon an algorithm which has been used before by others to solve the inverse eigenvalue problem for general real symmetric matrices and also for toeplitz matrices first we expose the structure of the eigenvectors of the so called generalized centrosymmetric matrices then we explore the properties of the eigenvectors to derive an efficient algorithm that is able to deliver a matrix with the required structure and spectrum we have implemented our ideas in a matlab code numerical results produced with this code are included

a generalization of the levinson algorithm for hermitian toeplitz matrices with any rank profile the paper describes a recursive algorithm for solving hermitian toeplitz systems of linear equations without any restriction on the ranks of their nested toeplitz subsystems such a general algorithm is needed e g to obtain the eigenfilters for signal processing applications or to compute the inverse of a nondefinite toeplitz matrix the regular portion of the algorithm is made of the classical levinson recursion the singular portion requires solving some well defined systems of linear equations with gradient structure the dimension of each of these sytems equals the amplitude of the corresponding singularity

the inverse eigenvalue problem for real symmetric toeplitz matrices we show that every set of n real numbers is the set of eigenvalues of an n x n real symmetric toeplitz matrix the matrix has a certain additional regularity the argument based on the topological degree is nonconstructive at t bell laboratories murray hill new jersey 07974 e mail address hjlfresearch att com this content downloaded from 157 55 39 29 on tue 12 apr 2016 08 53 54 utc all use subject to http about jstor org terms

boundary element solution for periodic acoustic problems abstract this work shows when using the boundary element method to solve 3d acoustic scattering problems from periodic structures the coefficient matrix can be represented as a block toeplitz matrix by exploiting the toeplitz structure the computational time and storage requirements to construct the coefficient matrix are significantly reduced to solve the linear system of equations the original matrix is embedded into a larger and more structured matrix called the block circulant matrix discrete fourier transform is then employed in an iterative algorithm to solve the block toeplitz system to demonstrate the effectiveness of the formulation for periodic acoustic problems two exterior acoustic case studies are considered the first case study examines a continuous structure to predict the noise generated by a sharp edged flat plate under quadrupole excitation directivity plots obtained using the periodic boundary element method technique are compared with numerical results obtained using a conventional boundary element model the second case study examines a discrete periodic structure to predict the acoustic performance of a sonic crystal noise barrier results for the barrier insertion loss are compared with both finite element results and available data in the literature

efimov spaces and the separable quotient problem for spaces cp k abstract the classic rosenthal lacey theorem asserts that the banach space c k of continuous real valued maps on an infinite compact space k has a quotient isomorphic to c or l 2 more recently kakol and saxon 20 proved that the space c p k endowed with the pointwise topology has an infinite dimensional separable quotient algebra iff k has an infinite countable closed subset hence c p n lacks infinite dimensional separable quotient algebras this motivates the following question does c p k admit an infinite dimensional separable quotient shortly sq for any infinite compact space k particularly does c p n admit sq our main theorem implies that c p k has sq for any compact space k containing a copy of n consequently this result reduces problem to the case when k is an efimov space i e k is an infinite compact space that contains neither a non trivial convergent sequence nor a copy of n although it is unknown if efimov spaces exist in zfc we show making use of some result of r de la vega 2008 under that for some efimov space k the space c p k has sq some applications of the main result are provided

adaptive tracking of multiple sinusoids whose power levels are widely separated the behavior of the gradient transversal filter lms the gradient lattice gl and the least squares lattice lsl when used to track multiple sinusoidal or narrow band components whose power levels are widely separated is investigated these approaches to the realization of the pth order one step linear predictor of the time series are recursive in time the lags of the instantaneous frequency estimates from their actual underlying values are of particular interest the frequency tracking characteristics of the lms gl and lsl algorithms are illustrated in several situations included are simulations of dual sinusoids undergoing a variety of frequency versus time dynamics and a formant tracking example of real speech

an eigenvalue recursion for toeplitz matrices in this correspondence a recursive algorithm for finding eigenvalues of a real symmetric toeplitz matrix from the eigenvalues of nested toeplitz submatrices is presented given the eigenvalues of two nested toeplitz submatrices the eigenvalues of the next larger toeplitz matrix can be found simply by solving a vandermonde set of equations and rooting two polynomials

weak sequential properties of johnson lindenstrauss spaces abstract a banach space x is said to have efremov s property e if every element of the weak closure of a convex bounded set c x is the weak limit of a sequence in c by assuming the continuum hypothesis we prove that there exist maximal almost disjoint families of infinite subsets of n for which the corresponding johnson lindenstrauss spaces enjoy resp fail property e this is related to a gap in plichko 2015 12 and allows to answer consistently questions of plichko and yost

an adaptive partition of unity method for chebyshev polynomial interpolation for a function that is analytic on and around an interval chebyshev polynomial interpolation provides spectral convergence however if the function has a singularity close to the interval the rate of convergence is near one in these cases splitting the interval and using piecewise interpolation can accelerate convergence chebfun includes a splitting mode that finds an optimal splitting through recursive bisection but the result has no global smoothness unless conditions are imposed explicitly at the breakpoints an alternative is to split the domain into overlapping intervals and use an infinitely smooth partition of unity to blend the local chebyshev interpolants a simple divide and conquer algorithm similar to chebfun s splitting mode can be used to find an overlapping splitting adapted to features of the function the algorithm implicitly constructs the partition of unity over the subdomains this technique is applied to explicitly given functions as well as to the solutions of singularly pertur

hamiltonian square roots of skew hamiltonian matrices abstract we present a constructive existence proof that every real skew hamiltonian matrix w has a real hamiltonian square root the key step in this construction shows how one may bring any such w into a real quasi jordan canonical form via symplectic similarity we show further that every w has infinitely many real hamiltonian square roots and give a lower bound on the dimension of the set of all such square roots some extensions to complex matrices are also presented

interlacement of the even and odd spectra of real symmetric toeplitz matrices it is shown that for every n the even and odd spectra of real symmetric toeplitz matrices tn tr s nr s 1 are interlaced if tr 1 0 cos r d r 0 1 2 where f is monotonic and nonconstant

a schur based algorithm for computing bounds to the smallest eigenvalue of a symmetric positive definite toeplitz matrix abstract recent progress in signal processing and estimation has generated c onsiderable interest in the problem of computing the smallest eigenvalue of symmetric positive definite toeplitz matrices several algorithms have been proposed in the literature they compute the smallest eigenvalue in an iterative fashion many of them relying on the levinson durbin solution of sequences of yule walker systems exploiting the properties of two algorithms recently developed for estimating a lower and an upper bound of the smallest singular value of upper triangular matrices respectively an algorithm for computing bounds to the smallest eigenvalue of a symmetric positive definite toeplitz matrix is derived the algorithm relies on the computation of the r factor of the qr factorization of the toeplitz matrix and the inverse of r the simultaneous computation of r and r 1 is efficiently accomplished by the generalized schur algorithm

an exact recursion for the composite nearest neighbor degeneracy for a 2 n lattice space a set theoretic argument is utilized to develop a recursion relation that yields exactly the composite nearest neighbor degeneracy for simple indistinguishable particles distributed on a 2 n lattice space the associated generating functions as well as the expectation of the resulting statistics are also treated

computing the smallest eigenpair of a symmetric positive definite toeplitz matrix an algorithm for computing the smallest eigenvalue of a symmetric positive definite toeplitz matrix is presented the eigenvalue is approximated from below by newton s method applied to the characteristic polynomial of the matrix the newton s step is calculated by a levinson durbin type recursion simultaneously this recursion produces a realistic error bound of the actual approximation without additional computing effort as well as a simple and efficient way to compute the associated eigenvector

initial values for the inverse toeplitz eigenvalue problem we show how to find a symmetric toeplitz matrix whose eigenvalues are close to a specified target set of n real numbers

centrosymmetric isospectral flows and some inverse eigenvalue problems this paper is concerned with the solution of some structured inverse eigenvalue problems in the class of centrosymmetric matrices for this aim isospectral flows evolving in the space of centrosymmetric matrices are considered to numerically construct a symmetric toeplitz matrix or a persymmetric hankel matrix from prescribed eigenvalues we establish a link between the two problems and we investigate the use of simultaneously diagonalizable algebra based on sine transform linear algebra appl 52 53 1983 992 to choose the starting centrosymmetric matrices for the isospectral flows some numerical tests show that our approach can tackle both problems when the solvability is guaranteed and it can give good insights when the existence of the solution is not guaranteed

fast algorithms for generalized displacement structures and lossless systems abstract we derive an efficient recursive procedure for the triangular factorization of strongly regular matrices with generalized displacement structure that includes as special cases a variety of previously studied classes such as toeplitz like and hankel like matrices the derivation is based on combining a simple gaussian elimination procedure with displacement structure and leads to a transmission like interpretation in terms of two cascades of first order sections we further derive state space realizations for each section and for the entire cascades and show that these realizations satisfy a generalized embedding result and a generalized notion of j losslessness the cascades turn out to have intrinsic blocking properties which can be shown to be equivalent to interpolation constrains

similarity of block companion and block toeplitz matrices a block companion matrix over a field of characteristic 0 is similar to a unique block unit upper hessenberg toeplitz matrix the proof is based on identities of formal power series and matrix representations of the shift of a polynomial model

on the exponentially slow motion of a viscous shock using formal asymptotic methods we study the internal layer behavior associated with the following viscous shock problem in the limit e 0 the convex nonlinearity f u satisfies f f for the steady problem we show that the method of matched asymptotic expansions fails to uniquely determine the location of the equilibrium shock layer solution this indeterminacy resulting from neglecting certain exponentially small effects is eliminated by using the projection method which exploits certain properties of the spectrum associated with the linearized operator for the time dependent problem we show that the viscous shock which is formed from initial data drifts towards the equilibrium solution on an exponentially long time interval of the order o ec e for some c 0 this exponentially slow behavior is analyzed by deriving an equation of motion for the location of the viscous shock for burgers equation f u u2 2 the results give an analytical characterization of the slow shock layer motion observed numerically in kreiss and kreiss see 11 we also show that the shock layer behavior is very sensitive to small changes in the boundary operator in addition using a wkb type method the slow viscous shock motion is studied numerically for small e the results comparing favorably with corresponding analytical results finally we relate the slow viscous shock motion to similar slow internal layer motion for the allen cahn equation

extension operators and twisted sums of c0 and c k spaces abstract we investigate the following problem posed by cabello sanchez castillo kalton and yost let k be a nonmetrizable compact space does there exist a nontrivial twisted sum of c 0 and c k i e does there exist a banach space x containing a non complemented copy y of c 0 such that the quotient space x y is isomorphic to c k using additional set theoretic assumptions we give the first examples of compact spaces k providing a negative answer to this question we show that under martin s axiom and the negation of the continuum hypothesis if either k is the cantor cube 2 1 or k is a separable scattered compact space of height 3 and weight 1 then every twisted sum of c 0 and c k is trivial we also construct nontrivial twisted sums of c 0 and c k for k belonging to several classes of compacta our main tool is an investigation of pairs of compact spaces k l which do not admit an extension operator c k c l

the asymptotic spectra of banded toeplitz and quasi toeplitz matrices toeplitz matrices occur in many mathematical as well as scientific and engineering investigations this paper considers the spectra of banded toeplitz and quasi toeplitz matrices with emphasis on n

eigenvalues and pseudo eigenvalues of toeplitz matrices the eigenvalues of a nonhermitian toeplitz matrix a are usually highly sensitive to perturbations having condition numbers that increase exponentially with the dimension n an equivalent statement is that the resolvent zz a of a toeplitz matrix may be much larger in norm than the eigenvalues alone would suggest exponentially large as a function of n even when z is far from the spectrum because of these facts the meaningfulness of the eigenvalues of nonhermitian toeplitz matrices for any but the most theoretical purposes should be considered suspect in many applications it is more meaningful to investigate the e pseudo eigenvalues the complex numbers z with ll zz a 11 l this paper analyzes the pseudospectra of toeplitz matrices and in particular relates them to the symbols of the matrices and thereby to the spectra of the associated toeplitz and laurent operators our results are reasonably complete in the triangular case and preliminary in the cases of nontriangular toeplitz matrices block toeplitz matrices and toeplitz like matrices with smoothly varying coefficients computed examples of pseudospectra are presented throughout and applications in numerical analysis are mentioned

networks for the weak topology of banach and frechet spaces abstract we start the systematic study of frechet spaces which are spaces in the weak topology a topological space x is an 0 space or an space if x has a countable k network or a locally finite k network respectively we are motivated by the following result of corson 1966 if the space c c x of continuous real valued functions on a tychonoff space x endowed with the compact open topology is a banach space then c c x endowed with the weak topology is an 0 space if and only if x is countable we extend corson s result as follows if the space e c c x is a frechet lcs then e endowed with its weak topology e e is an space if and only if e e e is an 0 space if and only if x is countable we obtain a necessary and some sufficient conditions on a frechet lcs to be an space in the weak topology we prove that a reflexive frechet lcs e in the weak topology e e is an space if and only if e e e is an 0 space if and only if e is separable we show however that the nonseparable banach space l 1 r with the weak topology is an space

an inverse eigenvalue problem and an associated approximation problem for generalized k centrohermitian matrices a partially described inverse eigenvalue problem and an associated optimal approximation problem for generalized k centrohermitian matrices are considered it is shown under which conditions the inverse eigenproblem has a solution an expression of its general solution is given in case a solution of the inverse eigenproblem exists the optimal approximation problem can be solved the formula of its unique solution is given

numerical solution of the inverse eigenvalue problem for real symmetric toeplitz matrices h j landau has recently given a nonconstructive proof of an existence theorem for the inverse eigenvalue problem for real symmetric toeplitz rst matrices this paper presents a procedure for the numerical solution of this problem the procedure is based on an implementation of newton s method that exploits landau s theorem and other special spectral properties of rst matrices with this version of newton s method together with the strategy proposed for applying it the method appears to be globally convergent however this is not proved

a two step inexact newton chebyshev like method for inverse eigenvalue problems abstract a two step inexact newton chebyshev like method is proposed to solve inverse eigenvalue problems unlike general newton type methods which need to invert the jacobian matrix that may lead to an unexpected instability the proposed method can guarantee the numerical stability by exploiting the chebyshev method to approximate the inverse of the jacobian matrix theoretically we prove that the proposed method converges cubically numerical examples are given to demonstrate the effectiveness of our method

approximate cayley transform methods for inverse eigenvalue problems and convergence analysis abstract based on an approximation to cayley transform we propose an approximate cayley transform method and its inexact version for solving inverse eigenvalue problems which has the advantage over other known methods in the sense that it avoids solving systems in obtaining the approximate eigenvectors under the nonsingular condition used in d sun and j sun 29 we show that the proposed methods converge at least superlinearly moreover numerical experiments are given which illustrate that comparing with the cayley transform methods our methods need much less inner iterations and cpu time

on the eigenvectors of symmetric toeplitz matrices this paper presents a number of results concerning the eigenvectors of a symmetric toeplitz matrix and the location of the zeros of the filters eigenfilters whose coefficients are the elements of the eigenvectors one of the results is that the eigenfilters corresponding to the maximum and minimum eigenvalues if distinct have their zeros on the unit circle while the zeros of the other eigenfilters may or may not have their zeros on the unit circle even if the zeros of the eigenfilters of a matrix are all on the unit circle the matrix need not be toeplitz examples are given to illustrate the different properties

perturbations of invariant subspaces of unreduced hessenberg matrices non structured perturbation of invariant subspaces of unreduced i e nonderogatory hessenberg matrices is considered some perturbation results for the generalized eigenvectors and the characteristic polynomial of unreduced upper hessenberg matrices are given two theorems are on the perturbation of invariant subspaces which are somewhat similar to the sin q theorems of davis and kahan apart from the residual which we do not have here dense perturbations of unreduced hessenberg matrices are also considered finally we prove an invariant subspace perturbation theorem for nonderogatory matrices

superfast tikhonov regularization of toeplitz systems toeplitz structured linear systems arise often in practical engineering problems correspondingly a number of algorithms have been developed that exploit toeplitz structure to gain computational efficiency when solving these systems the earliest fast algorithms for toeplitz systems required o n 2 operations while more recent superfast algorithms reduce the cost to o n log n 2 or below in this work we present a superfast algorithm for tikhonov regularization of toeplitz systems using an extension and transformation technique our algorithm translates a tikhonov regularized toeplitz system into a type of specialized polynomial problem known as tangential interpolation under this formulation we can compute the solution in only o n log n 2 operations we use numerical simulations to demonstrate our algorithm s complexity and verify that it returns stable solutions

on the eigenstructure of toeplitz matrices in spite of the fact that toeplitz eigenvalue problems have important applications in signal processing relatively little is known about the eigenstructure of finite real symmetric toeplitz matrices in this paper we exhibit two facts about the toeplitz eigenstructure problem first we show that any reciprocal or anti reciprocal n vector is an eigenvector for at least an n 1 2 dimensional linear space of real symmetric n n toeplitz matrices the second result is the fact that every n n toeplitz matrix can be imbedded into an n 1 n 1 toeplitz matrix which has a repeated smallest eigenvalue

on the eigenvalue problem for toeplitz band matrices abstract a formula is given for the characteristic polynomial of an n th order toeplitz band matrix with bandwidth k n in terms of the zeros of a k th degree polynomial with coefficients independent of n the complexity of the formula depends on the bandwidth k and not on the order n also given is a formula for eigenvectors in terms of the same zeros and k coefficients which can be obtained by solving a k k homogeneous system

is every matrix similar to a toeplitz matrix abstract we show that every n n complex nonderogatory matrix is similar to a unique unit upper hessenberg toeplitz matrix the proof is constructive and can be adapted to nonderogatory matrices with entries in any field of characteristic zero or characteristic greater than n we also prove that every n n complex matrix with n 4 is similar to a toeplitz matrix

on banach spaces whose norm open sets are fσ sets in the weak topology we investigate non separable banach spaces whose norm open sets are countable unions of sets closed in the weak topology and a narrower class of banach spaces with a network for the norm topology which is discrete in the weak topology in particular we answer a question of arhangel skii exhibiting various examples of non separable function spaces c k with a discrete network for the pointwise topology and consistently we answer some questions of edgar and oncina concerning borel structures and kadec renormings in banach spaces

an extension of matlab to continuous functions and operators an object oriented matlab system is described for performing numerical linear algebra on continuous functions and operators rather than the usual discrete vectors and matrices about eighty matlab functions from plot and sum to svd and cond have been overloaded so that one can work with our chebfun objects using almost exactly the usual matlab syntax all functions live on 1 1 and are represented by values at sufficiently many chebyshev points for the polynomial interpolant to be accurate to close to machine precision each of our overloaded operations raises questions about the proper generalization of familiar notions to the continuous context and about appropriate methods of interpolation differentiation integration zerofinding or transforms applications in approximation theory and numerical analysis are explored and possible extensions for more substantial problems of scientific computing are mentioned

inexact newton methods for inverse eigenvalue problems in this paper we survey some of the latest development in using inexact newton methods for solving inverse eigenvalue problems these methods require the solutions of nonsymmetric and large linear systems i e the large jacobian equations one can solve these systems by iterative methods inner iterations however iterative methods usually oversolve the problem in the sense that they require far more inner iterations than is required for the convergence of the newton outer iterations the inexact methods can avoid the oversolving problem and hence improve the efficiency the convergence rate of the inexact methods are superlinear and a good tradeoff between the required inner and outer iterations can be obtained

inverse eigenvalue problems a collection of inverse eigenvalue problems are identified and classified according to their characteristics current developments in both the theoretic and the algorithmic aspects are summarized and reviewed in this paper this exposition also reveals many open questions that deserve further study an extensive bibliography of pertinent literature is attached

a linear transformation and its properties with special applications in time series filtering abstract the main purpose of this paper is to introduce a linear transformation called t and to derive its algebraic properties by means of permutation matrices that represent it to demonstrate the importance of the t transformation for the estimation of latent variables in time series decomposition we obtain a general expression for smoothing matrices characterized by symmetric and asymmetric weighting systems we show that the submatrix of the symmetric weights to be applied to central observations is t invariant whereas the submatrices of the asymmetric weights to be applied to initial and final observations are the t transform of each other by virtue of this relation the properties of the t transformation provide useful information on the smoothing of time series data finally we illustrate the role of the t transformation on the weighting systems of several smoothers often applied for trend cycle estimation such as the locally weighted regression smoother loess the cubic smoothing spline the gaussian kernel and the 13 term trend cycle henderson filter

inverse spectral problem for pseudo jacobi matrices with partial spectral data in this paper we study a special kind of matrices which are pseudo jacobi matrices four inverse eigenvalue problems are discussed and the necessary and sufficient conditions are presented under which these problems are solvable the corresponding algorithms and some examples are given numerical results demonstrate that these methods are of practical utility

human ankle joint stiffness over the full range of muscle activation levels abstract system identification techniques have been used to track changes in dynamic stiffness of the human ankle joint over a wide range of muscle contraction levels subjects lay supine on an experimental table with their left foot encased in a rigid low inertia cast which was fixed to an electro hydraulic actuator operating as a position servo subjects generated tonic plantarflexor or dorsiflexor torques of different magnitudes ranging from rest to maximum voluntary contractions mvc during repeated presentations of a stochastic ankle angular position perturbation compliance impulse response functions irf were determined from every 2 5 s perturbation sequence the gain g natural freqency n and damping parameters of the second order model providing the best fit to each irf were determined and used to compute the corresponding inertial i viscous b and elastic k stiffness parameters the behaviour of these parameters with mean torque was found to follow two simple rules first the elastic parameter k increased in proportion to mean ankle torque as it was varied from rest to mvc these changes were considerable involving increases of more than an order of magnitude second the damping parameter remained almost invariant over the entire range of contractions despite the dramatic changes in k

sailing over three problems of koszmider abstract we discuss three problems of koszmider on the structure of the spaces of continuous functions on the stone compact k a generated by an almost disjoint family a of infinite subsets of we present a solution to two problems and develop previous results of marciszewski and pol answering the third one we will show in particular that assuming martin s axiom the space c k a is uniquely determined up to isomorphism by the cardinality of a whenever a c while there are 2 c nonisomorphic spaces c k a with a c we also investigate koszmider s problems in the context of the class of separable rosenthal compacta and indicate the meaning of our results in the language of twisted sums of c 0 and some c k spaces

not every matrix is similar to a toeplitz matrix abstract a negative answer to the question is every matrix similar to a toeplitz matrix raised by d s mackey n mackey and s petrovic linear algebra appl 297 1999 87 is given the tool of investigation is a result concerning the structure of the intersection of kernel and range of a toeplitz matrix which is of independent interest

levinson type algorithms for polynomial fitting and for cholesky and q factors of hankel and vandermonde matrices this paper presents levinson 1947 type algorithms for i polynomial fitting ii obtaining a q decomposition of vandermonde matrices and a cholesky factorization of hankel matrices iii obtaining the inverse of hankel matrices the algorithm for the least squares solution of hankel systems of equations requires 3n sup 2 9n 3 multiply and divide operation mdo the algorithm for obtaining an orthogonal representation of an m spl times n vandermonde matrix x and computing the cholesky factors f of hankel matrices requires 5mn n sup 2 2n 3m mdo and the algorithm for generating the inverse of hankel matrices requires 3 n sup 2 n 2 2 mdo our algorithms have been tested by means of fitting of polynomials of various orders and fortran versions of all subroutines are provided in the appendix

twisted sums of c0 and c k spaces a solution to the ccky problem abstract we consider the class of banach spaces y for which c 0 admits a nontrivial twisted sum with y we present a characterization of such spaces y in terms of properties of the w e a k topology on y we prove that under the continuum hypothesis c 0 has a nontrivial twisted sum with every space of the form y c k where k is compact and not metrizable this gives a consistent affirmative solution to a problem posed by cabello castillo kalton and yost