the discriminance for a special class of circulant matrices and their diagonalization abstract this paper deals with a new type of matrices the structure of this class of matrices is similar to circulant matrix we call it h circulant matrix furthermore the sum the difference the product the inverse and the adjoint matrix of these matrices are also h circulant matrixes we not only give six discriminance for h circulant matrices but also discuss the diagonalization and nonsingularity of these matrices finally author gives a numerical example

practical variance reduction via regression for simulating diffusions the well known variance reduction methods the method of importance sampling and the method of control variates can be exploited if an approximation of the required solution is known here we employ conditional probabilistic representations of solutions together with the regression method to obtain sufficiently inexpensive although rather rough estimates of the solution and its derivatives by using the single auxiliary set of approximate trajectories starting from the initial position these estimates can effectively be used for significant reduction of variance and further accurate evaluation of the required solution the developed approach is supported by numerical experiments

technical communique predictor based stabilization of discrete time varying input delay systems this paper adapts some literature results on stabilizing discrete time varying input delay systems to the case of having a predictor based controller the objective of the paper is showing that the incorporation of predictors to the referred results is relatively simple and by means of such predictors robustness against delay mismatch in the input channel may be improved in this way larger delay variation margins are proved with predictors when compared to standard memoryless state feedback as intuitively expected due to the extra past information available

on computing of arbitrary positive integer powers for one type of odd order tridiagonal matrices with two zero rows and eigenvalues on imaginary axis i abstract in this paper we derive the general expression of the lth power l n l 2 for one type of tridiagonal matrices of order n 2p 1 p n p 2

on computing the determinants and inverses of some special type of tridiagonal and constant diagonals matrices the determinants and inverses of some tridiagonal and constant diagonals matrices are discussed in the paper linear recurrence equations of the second and higher orders which satisfy these determinants are presented here in connection with these determinants new families of polynomials are defined the relationships between these polynomials and normed chebyshev polynomials of the first and second kind are investigated incidentally a number of new identities for chebyshev polynomials and some linear modifications of these polynomials are shown as well as many new trigonometric identities and identities for fibonacci and lucas numbers

multilevel monte carlo path simulation we show that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using monte carlo path simulations in the simplest case of a lipschitz payoff and a euler discretisation the computational cost to achieve an accuracy of o e is reduced from o e 3 to o e 2 log e 2 the analysis is supported by numerical results showing significant computational savings

on computing of arbitrary positive integer powers for one type of symmetric tridiagonal matrices of odd order i in this paper we derive the general expression of the lth power l n for one type of symmetric tridiagonal matrices of order n 2p 1 p n

technical communique improved stability criterion and its applications in delayed controller design for discrete time systems this paper is concerned with the problem of delay dependent stability analysis for discrete time systems with interval like time varying delays and the problem of stabilization for discrete time linear systems via time delayed controllers the first problem is solved by applying a novel lyapunov functional and an improved delay dependent stability criterion is obtained in terms of a linear matrix inequality based on this a sufficient condition for the solvability of the second problem is presented the reduced conservatism of the proposed stability result is shown through a numerical example while the applicability of the time delayed controller design method is demonstrated by an inverted pendulum system

on computing of arbitrary positive integer powers for one type of even order symmetric circulant matrices ii abstract this article is an extension of the work j rimas on computing of arbitrary positive integer powers for one type of even order symmetric circulant matrices i appl math comput in press in which the general expression of the l th power l n for one type of even order symmetric circulant matrices is given in this new paper we present the complete derivation of this general expression expressions of eigenvectors and of the transforming matrix and its inverse are given too

positive integer powers and inverse for one type of even order symmetric pentadiagonal matrices in this study we derive the general expression for the entries of the qth power q n for one type of even order symmetric pentadiagonal matrices

on computing of arbitrary positive integer powers for one type of tridiagonal matrices of even order abstract this paper is an extension of the work on computing of arbitrary positive integer powers for one type of tridiagonal matrices applied mathematics and computation to appear in which the general expression of the l th power l n for one type of tridiagonal matrices of order n 2 p 1 p n is presented in this new paper we derive the general expression of the l th power l n for the same type of tridiagonal matrices of order n 2 p p n expressions of eigenvectors and jordan s form of the matrix and of transforming matrix and its inverse are given too

on the bounds for the norms of r circulant matrices with the fibonacci and lucas numbers abstract in this paper we have found upper and lower bounds for the spectral norms of r circulant matrices in the forms a c r f 0 f 1 f n 1 b c r l 0 l 1 l n 1 and we have obtained some bounds for the spectral norms of kronecker and hadamard products of a and b matrices

variance reduction for discretised diffusions via regression abstract in this paper we present a novel approach towards variance reduction for discretised diffusion processes the proposed approach involves specially constructed control variates and allows for a significant reduction in the variance for the terminal functionals in this way the complexity order of the standard monte carlo algorithm e 3 in the case of a first order scheme and e 2 5 in the case of a second order scheme can be reduced down to e 2 for any 0 0 25 with e being the precision to be achieved these theoretical results are illustrated by several numerical examples

the computation of the square roots of circulant matrices abstract in the first part of this paper we investigate the reduced forms of circulant matrices and quasi skew circulant matrices by using their properties we present two efficient algorithms to compute the square roots of circulant matrices and quasi skew circulant matrices respectively those methods are faster than the traditional algorithm which is based on the schur decomposition in the second part we further consider circulant h matrices with positive diagonal entries and develop two algorithms for computing their principal square roots those two algorithms have the common advantage that is they only need matrix matrix multiplications in their iterative sequences an operation which can be done very efficiently on modern high performance computers

preconditioners for ill conditioned toeplitz systems constructed from positive kernels in this paper we are interested in the iterative solution of ill conditioned toeplitz systems generated by continuous nonnegative real valued functions f with a finite number of zeros we construct new w circulant preconditioners without explicit knowledge of the generating function f by approximating f by its convolution f kn with a suitable positive reproducing kernel kn by the restriction to positive kernels we obtain positive definite preconditioners moreover if f has only zeros of even order le 2s then we can prove that the property int pi pi t 2k k n t mbox d t le c n 2k k 0 hspace 1 5pt ldots s of the kernel is necessary and sufficient to ensure the convergence of the pcg method in a number of iteration steps independent of the dimension n of the system our theoretical results were confirmed by numerical tests

on computing the eigenvectors of a class of structured matrices a real symmetric matrix of order n has a full set of orthogonal eigenvectors the most used approach to compute the spectrum of such matrices reduces first the dense symmetric matrix into a symmetric structured one i e tridiagonal matrices or semiseparable matrices this step is accomplished in o n 3 operations once the latter symmetric structured matrix is available its spectrum is computed in an iterative fashion by means of the qr method in o n 2 operations in principle the whole set of eigenvectors of the latter structured matrix can be computed by means of inverse iteration in o n 2 operations the blemish in this approach is that the computed eigenvectors may not be numerically orthogonal if clusters are present in the spectrum to enforce orthogonality the gram schmidt procedure is used requiring o n 3 operations in the worst case in this paper a fast and stable method to compute the eigenvectors of tridiagonal and semiseparable matrices which does not suffer from the loss of orthogonality due to the presence of clusters in the spectrum is presented the algorithm requires o n 2 floating point operations if clusters of small size are present in the spectrum

on a constant diagonals matrix in this paper we consider a constant diagonals matrix the matrix was discussed in witula and slota r witula d slota on computing the determinants and inverses of some special type of tridiagonal and constant diagonals matrices appl math comput 189 1 2007 514 527 the authors gave some results on determinant and the inverse of the matrix for some special cases we give lu factorization and then compute determinant of the matrix we determine eigenvalues of the matrix further we obtain some relationships between permanent of the matrix and terms of a certain recurrence relation

on computing of arbitrary positive integer powers for tridiagonal matrices with elements 1 0 0 0 1 in principal and 1 1 1 1 in neighbouring diagonals ii this paper is an extension of the work j rimas on computing of arbitrary positive integer powers for tridiagonal matrices with elements 1 0 0 0 1 in principal and 1 1 1 1 in neighbouring diagonals i applied mathematics and computation in press doi 10 1016 j amc 2006 07 145 in which the general expression of the lth power l n for one type of tridiagonal matrices of arbitrary order is given in this new paper we present the complete derivation of this general expression expressions of eigenvectors of the matrix and of the transforming matrix and its inverse are given too

on computing of arbitrary positive integer powers for one type of odd order symmetric circulant matrices ii this article is an extension of the work j rimas on computing of arbitrary positive integer powers for one type of symmetric odd order circulant matrices i appl math comput in press in which the general expression of the lth power email protected n for one type of symmetric odd order circulant matrices is given in this new paper we present the complete derivation of this general expression expressions of eigenvectors and jordan s form of the matrix and of the transforming matrix and its inverse are given too

on computing of arbitrary positive powers for anti tridiagonal matrices of even order abstract in this paper the general expression of the lth power l n for one type of anti tridiagonal matrices is derived expressions of eigenvectors and jordan s form of the matrix and of the transforming matrix and its inverse are given

singular value decomposition for bidiagonal filter matrices in this paper we present a singular value decomposition for any n n 1 complex upper bidiagonal toeplitz matrix

on computing of arbitrary positive integer powers for one type of tridiagonal matrices in this paper we derive the general expression of the l th power email protected n for one type of tridiagonal matrices of order n 2p 1 email protected n

a unifying approach to some old and new theorems on distribution and clustering abstract a unifying approach is proposed to studying the distributions of eigenvalues and singular values of toeplitz matrices associated with a fourier series and multilevel toeplitz matrices associated with a multidimensional fourier series obtained are the extensions of the szego and avram parter theorems where the generating function is now required to belong to l 2 and not necessarily to l analogous extensions are given for multilevel toeplitz matrices in particular it is proved that if f x 1 x p l 2 then the p level complex toeplitz matrices allied with f have their singular values distributed as f x 1 x p the distribution results for the cesaro optimal circulants hold even if f l 1 also suggested are new theorems on clustering that have to do with the preconditioning of multilevel toeplitz matrices by multilevel circulants

new stability criteria for linear discrete time systems with interval like time varying delays this technical note is concerned with stability of linear discrete time systems with interval like time varying delays two new stability criteria are derived by constructing a new lyapunov functional and utilizing two novel techniques for estimating the forward difference of the lyapunov functional the relationship between these stability criteria and some existing ones is established through the relationship it is clear that these stability criteria are less conservative than some existing ones which is confirmed by a numerical example

binomial coefficients and powers of large tridiagonal matrices with constant diagonals in this paper we derive a general expression for the entries of the qth power email protected n of the nxn complex tridiagonal matrix tridiag n a 1 a 0 a 1 for all n 2 q 1 in terms of binomial coefficients

cubature on wiener space it is well known that there is a mathematical equivalence between solving parabolic partial differential equations pdes and the integration of certain functionals on wiener space monte carlo simulation of stochastic differential equations sdes is a naive approach based on this underlying principle in finite dimensions it is well known that cubature can be a very effective approach to integration we discuss the appropriate extension of this idea to wiener space in the process we develop high order numerical schemes valid for high dimensional sdes and semi elliptic pdes

a note on the fast algorithm for block toeplitz systems with tensor structure we study the solutions of block toeplitz systems t m nx b by using the preconditioned conjugate gradient pcg method here t m n t m t n and t i i m n are toeplitz matrices in x jin appl math comput 73 1995 115 124 jin introduced a fast algorithm for these systems by applying the pcg method this fast algorithm allows a tensor problem to be reduced to a one dimensional problem it was proved that if the mn by mn system is well conditioned then the pcg method converges superlinearly and only o mnlogmn operations are required in solving the preconditioned system however only well conditioned systems were considered in jin 1995 in this paper we apply this fast algorithm with the w circulant preconditioners proposed in d potts g steidl preconditioners for ill conditioned toeplitz matrices bit to be appeared to solve the ill conditioned systems numerical results are included to illustrate the effectiveness of the algorithm for solving the preconditioned systems by using the pcg method an application in image restoration is also given

on computing of positive integer powers for r circulant matrices in this paper we give a method of computing arbitrary positive integer powers for arbitrary order r circulant matrices by using the basis expression of r circulant matrices in matrix spaces and the multinomial theorem

a note on computing of positive integer powers for circulant matrices koken et al positive integer powers for one type of odd order circulant matrices appl math comput 217 2011 4377 4381 proposed the general expression of the qth power for one type of odd order circulant matrices in this paper we give another method to computing arbitrary positive integer powers for arbitrary order circulant matrices it is shown that this method is simpler than koken s method

technical communique robust stabilization of linear discrete time systems with time varying input delay this paper presents a sufficient condition to stabilize linear discrete time systems with time varying input delay and model uncertainties the key idea consists of applying artstein s reduction method and the scaled bounded real lemma the robust stabilization problem is cast as a set of linear matrix inequalities on a transformed delay free system hence a novel convex characterization of the problem an alternative to bilinear matrix inequalities in prior literature is provided predictor based controllers and robust state feedback stabilization are particular cases of the proposal furthermore numerical examples show that this proposal may improve tolerance against delay variations when compared to other methods available in literature

on computing of arbitrary positive integer powers for one type of even order skew symmetric tridiagonal matrices with eigenvalues on imaginary axis ii this paper is an extension of the work on computing of arbitrary positive integer powers for one type of even order skew symmetric tridiagonal matrices with eigenvalues on imaginary axis i appl math comput in press in which the general expression of the lth power l n for one type of tridiagonal matrices of order n 2p p n is given in this new paper we present the complete derivation of this general expression expressions of eigenvectors of the matrix and of the transforming matrix and its inverse are given too

positive integer powers for one type of odd order circulant matrices article i nfo abstract in this study we derive the general expression for the entries of the qth power q 2 n for

variance reduction for simulated diffusions this article develops some variance reduction techniques for the monte carlo integration of functionals of the solutions of ito stochastic differential equations sdes the monte carlo method for sdes offers a means of calculating solutions to certain types of parabolic partial differential equation and so has applications in various fields including stochastic control particle physics and econometrics it involves the representation of the required integrals as means of random variables defined on infinite dimensional wiener spaces which cannot be simulated directly sthey must at some stage be approximated by variables defined on high but finite dimensional spaces the approach taken here is to construct variance reduced random variables on the infinite dimensional spaces which can subsequently be approximated by any of a number of known finite difference methods the methods of control variates and importance sampling are developed in both cases a perfect variate i e one which is unbiased and h

on the powers and the inverse of a tridiagonal matrix in this paper we present an eigendecomposition of a tridiagonal matrix tridiagonal matrix powers and inverse are derived as consequence we get some relations verified by the coefficients of the inverse and the powers of a tridiagonal matrix

construction of preconditioners for wiener hopf equations by operator splitting abstract in this paper we propose a new type of preconditioners for solving finite section wiener hopf integral equations i a x g by the preconditioned conjugate gradient algorithm we show that for an integer u 1 the operator i a can be decomposed into a sum of operators i p u v for 0 v 1 u v i p u v 1 thus the way the preconditioners are constructed is very similar to the approach used in the additive schwarz method for elliptic problems as for the convergence rate we prove that the spectra of the resulting preconditioned operators 1 u v i p u v 1 i a are clustered around 1 and thus the algorithm converges sufficiently fast finally we discretize the resulting preconditioned equations by rectangular rule numerical results show that our methods converges faster than those preconditioned by using circulant integral operators

positive integer powers of complex skew symmetric circulant matrices abstract in j rimas on computing of arbitrary positive integer powers for one type of odd order symmetric circulant matrices i applied mathematics and computation 165 2005 137 141 j rimas on computing of arbitrary positive integer powers for one type of even order symmetric circulant matrices i applied mathematics and computation 172 2006 86 90 rimas derived a general expression for the entries of the qth power q n of the n n real symmetric circulant matrix circ n 0 1 0 0 0 0 1 for all n n in this paper we present an extension of that interesting work deriving a similar expression for the entries of the positive integer powers of any complex symmetric circulant matrix

linear systems with delayed controls a reduction linear systems with delayed control action are transformed into systems without delays under an absolute continuity condition the new system is an ordinary differential control equation in the general case the new system is a measure differential control system it is shown how the controllability stabilization and various optimization problems can be analyzed via the reduced systems

positive integer powers of certain complex tridiagonal matrices in this paper we firstly present a general expression for the entries of the rth email protected n power of a certain n square complex tridiagonal matrix in terms of the chebyshev polynomials of the first kind secondly we obtain a complex factorization formula for generalized fibonacci pell numbers obeying also classical fibonacci and pell numbers

a new model transformation of discrete time systems with time varying delay and its application to stability analysis this technical note focuses on analyzing a new model transformation of uncertain linear discrete time systems with time varying delay and applying it to robust stability analysis the uncertainty is assumed to be norm bounded and the delay intervally time varying a new comparison model is proposed by employing a new approximation for delayed state and then lifting method and simple lyapunov krasovskii functional method are used to analyze the scaled small gain of this comparison model this new approximation results in a much smaller error than the existing ones based on the scaled small gain theorem new stability criteria are proposed in terms of linear matrix inequalities moreover it is shown that the obtained conditions can be established through direct lyapunov method two numerical examples are presented to illustrate the effectiveness and superiority of our results over the existing ones

a convex characterization of gain scheduled h sub spl infin controllers an important class of linear time varying systems consists of plants where the state space matrices are fixed functions of some time varying physical parameters spl theta small gain techniques can be applied to such systems to derive robust time invariant controllers yet this approach is often overly conservative when the parameters spl theta undergo large variations during system operation in general higher performance can be achieved by control laws that incorporate available measurements of spl theta and therefore adjust to the current plant dynamics this paper discusses extensions of h sub spl infin synthesis techniques to allow for controller dependence on time varying but measured parameters when this dependence is linear fractional the existence of such gain scheduled h sub spl infin controllers is fully characterized in terms of linear matrix inequalities the underlying synthesis problem is therefore a convex program for which efficient optimization techniques are available the formalism and derivation techniques developed here apply to both the continuous and discrete time problems existence conditions for robust time invariant controllers are recovered as a special case and extensions to gain scheduling in the face of parametric uncertainty are discussed in particular simple heuristics are proposed to compute such controllers

positive integer powers of certain tridiagonal matrices abstract in j rimas on computing of arbitrary positive integer powers for one type of symmetric tridiagonal matrices of even order i appl math comput 168 2005 783 787 and j rimas on computing of arbitrary positive integer powers for one type of symmetric tridiagonal matrices of odd order i appl math comput 171 2005 1214 1217 rimas derived a general expression for the entries of the qth power q n of the n n real symmetric tridiagonal matrix tridiag n 1 0 1 for all n n in this paper we present an extension of that interesting work deriving a similar expression for the entries of the qth power q n of the n n hermitian tridiagonal matrix tridiag n a 1 a 0 a 1 for all n n

a multi temperature kinetic ising model and the eigenvalues of some perturbed jacobi matrices in this paper we analyze the eigenvalues of some perturbed jacobi matrices the results contain as particular cases the known spectra of several classes of tridiagonal matrices studied recently as a motivation we discuss a three and a four temperature kinetic ising model that can be analyzed using some perturbed jacobi matrices the analytical results can also be used for the associated reaction diffusion systems to solve for the particle density

on computing of arbitrary positive integer powers for one type of even order symmetric circulant matrices i abstract in this paper we derive the general expression of the l th power l n for one type of symmetric circulant matrices of order n 2 p p n p 2

technical communique a delay partitioning approach to the stability analysis of discrete time systems this paper revisits the problem of stability analysis for linear discrete time systems with time varying delay in the state by utilizing the delay partitioning idea new stability criteria are proposed in terms of linear matrix inequalities lmis these conditions are developed based on a novel lyapunov functional in addition to delay dependence the obtained conditions are also dependent on the partitioning size we have also established that the conservatism of the conditions is a non increasing function of the number of partitions numerical examples are given to illustrate the effectiveness and advantage of the proposed methods