central simple superalgebras with anti automorphisms of order two of the first kind by a theorem of albert s a central simple associative algebra has an involution of the first kind if and only if it is of order 2 in the brauer group our main purpose is to develop the theory of existence of anti automorphisms of order 2 of the first kind on finite dimensional central simple associative superalgebras over k where k is a field of arbitrary characteristic first we need to generalize the skolem noether theorem to the superalgebra case then we show which kind of finite dimensional central simple superalgebras have an anti automorphism of order 2 of the first kind

approximate factorization constraint preconditioners for saddle point matrices we consider the application of the conjugate gradient method to the solution of large symmetric indefinite linear systems special emphasis is put on the use of constraint preconditioners and a new factorization that can reduce the number of flops required by the preconditioning step results concerning the eigenvalues of the preconditioned matrix and its minimum polynomial are given numerical experiments validate these conclusions

a robust preconditioner with low memory requirements for large sparse least squares problems this paper describes a technique for constructing robust preconditioners for the cgls method applied to the solution of large and sparse least squares problems the algorithm computes an incomplete ldlt factorization of the normal equations matrix without the need to form the normal matrix itself the preconditioner is reliable pivot breakdowns cannot occur and has low intermediate storage requirements numerical experiments illustrating the performance of the preconditioner are presented a comparison with incomplete qr preconditioners is also included

a theory of pseudoskeleton approximations abstract let an m n matrix a be approximated by a rank r matrix with an accuracy e we prove that it is possible to choose r columns and r rows of a forming a so called pseudoskeleton component which approximates a with o e r m n accuracy in the sense of the 2 norm on the way to this estimate we study the interconnection between the volume i e the determinant in the absolute value and the minimal singular value r of r r submatrices of an n r matrix with orthogonal columns we propose a lower bound better than one given by chandrasekaran and ipsen and by hong and pan for the maximum of r over all these submatrices and formulate a hypothesis on a tighter bound

the exponent for superalgebras with superinvolution abstract let a be a superalgebra with superinvolution over a field of characteristic zero and let c n a n 1 2 be its sequence of codimensions in 6 it was proved that such a sequence is exponentially bounded in this paper we capture this exponential growth for finitely generated superalgebras with superinvolution a over an algebraically closed field of characteristic zero we shall prove that lim n c n a n exists and it is an integer denoted exp a and called exponent of a moreover we shall characterize finitely generated superalgebras with superinvolution according to their exponent

maximal subalgebras of associative superalgebras abstract the maximal subalgebras of the finite dimensional central simple associative superalgebras possibly endowed with a superinvolution are determined this relies on the corresponding description by m racine in the ungraded case which is completed here too

fir filters and recursive forms for continuous time invariant state space models an fir finite impulse response filter and an fir smoother are introduced for continuous time invariant state space models it is shown in this note that finite impulse responses of the fir filter and smoother can be easily determined by solving a simple riccati type matrix differential equation on a finite interval especially for systems with stationary processes finite impulse responses of the fir filter and smoother become time invariant and can be computed from simpler equations for fast computational purposes recursive forms of the fir filter and smoother are derived by using adjoint variables in this case all gains for recursive forms are shown to be constant

semiprime prime and simple jordan superpairs covered by grids in this paper we continue the investigation of jordan superpairs covered by a grid which have recently been described by the second author e neher j algebra 269 2003 28 73 for such a jordan superpair we characterize semiprimeness primeness and simplicity in terms of its associated supercoordinate system

optimal memory for discrete time fir filters in state space in this correspondence we propose an efficient estimator of optimal memory averaging interval for discrete time finite impulse response fir filters in state space its crucial property is that only real measurements and the filter output are involved with no reference and noise statistics testing by the two state polynomial model has shown a very good correspondence with predicted values even in the worst case of the harmonic model the estimator demonstrates practical applicability

h_2 output feedback control with finite multiple measurement information this paper proposes a new h 2 output feedback control with finite multiple measurement information for discrete time systems with disturbances this control is called an h 2 finite multiple measurement output feedback control h2fmmofc the new control ascertains the h 2 performance for disturbances and the equivalence to the h 2 state feedback control without disturbances on a finite measurement horizon the boundedness and exponential stability of the proposed h2fmmofc are also investigated the gain matrices of the h2fmmofc are obtained by solving a convex problem utilizing the linear matrix inequality tool via a numerical example the h2fmmofc is shown to ensure the h 2 performance as well as the excellent robustness property against unexpected temporary model uncertainty although the uncertainty is not considered in its design

design of rls fir filter using covariance information in linear continuous time stochastic systems this paper addresses a new design method of recursive least squares rls and finite impulse response fir filter using covariance information in linear continuous time stochastic systems the signal process is observed with additive white noise it is assumed that the white observation noise is independent of the signal process the auto covariance function of the signal is expressed in the semi degenerate kernel form the rls fir filter uses the following information 1 the auto covariance function of the signal expressed in the semi degenerate kernel form 2 the variance of the white observation noise process 3 the observed values

group gradings on superinvolution simple superalgebras in this paper we describe all group gradings by an arbitrary finite group g on non simple finite dimensional superinvolution simple associative superalgebras over an algebraically closed field f of characteristic 0 or coprime to the order of g

primitive superalgebras with superinvolution abstract our main purpose is to provide for primitive associative superalgebras a structure theory analogous to that for algebras 5 6 10 and to classify primitive superrings with superinvolution having a minimal one sided superideal we were led to this problem by our work on finite dimensional central simple jordan superalgebras over fields of characteristic not 2 9 see also 7 of course just as symmetric elements give rise to jordan superalgebras skewsymmetric elements give rise to lie superalgebras 8 4 the results and methods are closely related to those of structure theory of associative rings and central simple associative algebras with involution 5 chap i 6 chaps ii iii 1 chap x 10 chap 2 some of the results have been announced in 13

on maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices abstract the problem of finding a k k submatrix of maximum volume of a matrix a is of interest in a variety of applications for example it yields a quasi best low rank approximation constructed from the rows and columns of a we show that such a submatrix can always be chosen to be a principal submatrix not only for symmetric semidefinite matrices but also for diagonally dominant matrices then we analyze the low rank approximation error returned by a greedy method for volume maximization cross approximation with complete pivoting our bound for general matrices extends an existing result for symmetric semidefinite matrices and yields new error estimates for diagonally dominant matrices in particular for doubly diagonally dominant matrices the error is shown to remain within a modest factor of the best approximation error we also illustrate how the application of our results to cross approximation for functions leads to new and better convergence results

standard polynomials and matrices with superinvolutions abstract let m n f be the algebra of n n matrices over a field f of characteristic zero the superinvolutions on m n f were classified by racine in 12 they are of two types the transpose and the orthosymplectic superinvolution this paper is devoted to the study of polynomial identities satisfied by m n f the goal is twofold on one hand we determine the minimal degree of a standard polynomial vanishing on suitable subsets of symmetric or skew symmetric matrices for both types of superinvolutions on the other in case of m 2 f we find generators of the ideal of identities and we compute the corresponding sequences of cocharacters and codimensions

linear optimal fir estimation of discrete time invariant state space models this paper addresses a general p shift linear optimal finite impulse response fir estimator intended for solving universally the problems of filtering p 0 smoothing p 0 of discrete time invariant models in state space an optimal solution is found in the batch form with the initial mean square state function self determined by solving the discrete algebraic riccati equation an unbiased solution represented both in the batch and recursive forms does not involve any knowledge about noise and initial state the mean square errors in both the optimal and unbiased estimates are found via the noise power gain npg and a recursive algorithm for fast computation of the npg is supplied applications are given for fir filtering with fixed receding and full averaging horizons

preconditioning linear least squares problems by identifying a basis matrix we study the solution of the linear least squares problem min x b a x 2 2 where the matrix a in bbb r m times n m ge n has rank n and is large and sparse we assume that a is available as a matrix not an operator the preconditioning of this problem is difficult because the matrix a does not have the properties of differential problems that make standard preconditioners effective incomplete cholesky techniques applied to the normal equations do not produce a well conditioned problem we attempt to bypass the ill conditioning by finding an n times n nonsingular submatrix b of a that reduces the euclidean norm of ab 1 we use b to precondition a symmetric quasi definite linear system whose condition number is then independent of the condition number of a and has the same solution as the original least squares problem we illustrate the performance of our approach on some standard test problems and show it is competitive with other approaches

fir filters and recursive forms for discrete time state space models abstract an fir finite impulse response filter and an fir smoother are introduced for discrete time state space models with system noise the fir structure not only guarantees both the bibo stability and the robustness to some parameter changes but also improves the filter divergence problem it is shown in this paper that impulse responses of both the fir filter and the fir smoother are easily obtained from riccati type difference equations especially for time invariant state space models they are also to be time invariant and finally determined by simple equations on a finite interval for the purpose of implementation recursive forms of the fir filter and smoother are derived using each other as adjoint variables improved characteristics of the fir filter in the divergence problem are demonstrated via a simulation

recursive limited memory filtering and scattering theory corresp redheffer scattering theory is reviewed in a generalized setting as a method to derive recursive solutions of linear two point boundary value problems tpbvp over arbitrarily varying intervals the results can be used to derive a complete solution for the problem of limited memory or sliding window estimation when a usual state space model for the signal is available recursive limited memory filters are derived for both continuous and discrete time signals

rectangular maximum volume submatrices and their applications abstract we introduce a definition of the volume of a general rectangular matrix which is equivalent to an absolute value of the determinant for square matrices we generalize results of square maximum volume submatrices to the rectangular case show a connection of the rectangular volume with an optimal experimental design and provide estimates for a growth of coefficients and an approximation error in spectral and chebyshev norms three promising applications of such submatrices are presented recommender systems finding maximal elements in low rank matrices and preconditioning of overdetermined linear systems the code is available online

suboptimal fir filtering of nonlinear models in additive white gaussian noise the first and second order extended finite impulse response efir1 and efir2 respectively filters are addressed for suboptimal estimation of nonlinear discrete time state space models with additive white gaussian noise it is shown that unlike the extended kalman filter ekf and efir2 filter the efir1 one does not require noise statistics and initial errors only within a narrow region around actual noise covariances efir filters fall a bit short of ekf and they demonstrate better performance otherwise it is shown that the optimal averaging interval for efir filters can be determined via measurement without a reference model in a learning cycle we also notice that the second order approximation can improve the local performance but it can also deteriorate it we thus have no recommendations about its use at least for tracking considered as an example of applications

a receding horizon kalman fir filter for discrete time invariant systems a receding horizon kalman fir filter is presented that combines the kalman filter and the receding horizon strategy when the horizon initial state is assumed to be unknown the suggested filter is a fir filter form which has many good inherent properties it can always be defined irrespective of singularity problems caused by unknown information about the horizon initial state the suggested filter can be represented in either an iterative form or a standard fir form it is also shown that the suggested filter possesses the unbiasedness property and the remarkable deadbeat property irrespective of any horizon initial condition the validity of the suggested filter is illustrated by numerical examples

l_2 e fir filters for deterministic continuous time state space signal models in this paper a new l2 e performance criterion is introduced which is represented as a gain between the disturbance during the recent time interval and the current estimation error based on the l2 e performance criterion the l2 e finite impulse response fir filter leff is proposed for deterministic continuous time state space signal models without requiring the stochastic information such as variances and means the leff is designed to minimize the maximum value of the l2 e performance criterion together with prior constraints such as linearity unbiased property in the deterministic sense and fir structure simultaneously via simulation the leff is compared with other deterministic infinite impulse response iir filters such as the hinfin and l2 linfin filters

a receding horizon kalman fir filter for linear continuous time systems a receding horizon kalman finite impulse response fir filter is suggested for continuous time systems combining the kalman filter with the receding horizon strategy in the suggested filter the horizon initial state is assumed to be unknown it can always be obtained irrespective of unknown information on the horizon initial state the filter may be the first stochastic fir form for continuous time systems that may have many good inherent properties the suggested filter can be represented in an iterative form and also in a standard fir form the suggested filter turns out to be a remarkable deadbeat observer the validity of the suggested filter is illustrated by numerical examples

a new solution to the induced l finite impulse response filtering problem based on two matrix inequalities in this paper we use an induced l approach to create a new filter with a finite impulse response fir structure for state space models with external disturbances this filter is called an induced l fir filter iliff the proposed iliff s gain matrix can be determined by solving a linear matrix inequality problem for a fixed positive scalar variable an illustrative example is given to demonstrate the effectiveness of the iliff