the new upper bounds on the spectral radius of weighted graphs abstract let us consider weighted graphs where the weights of the edges are positive definite matrices the eigenvalues of a weighted graph are the eigenvalues of its adjacency matrix and the spectral radius of a weighted graph is also the spectral radius of its adjacency matrix in this paper we obtain two upper bounds for the spectral radius of weighted graphs and compare with a known upper bound we also characterize graphs for which the upper bounds are attained

where is the nearest non regular pencil abstract this is a first step toward the goal of finding a way to calculate a smallest norm deregularizing perturbation of a given square matrix pencil minimal de regularizing perturbations have geometric characterizations that include a variable projection linear least squares problem and a minimax characterization reminiscent of the courant fischer theorem the characterizations lead to new computationally attractive upper and lower bounds we give a brief survey and illustrate strengths and weaknesses of several upper and lower bounds some of which are well known and some of which are new the ultimate goal remains elusive

spectra of digraphs in this primarily expository paper we survey classical and some more recent results on the spectra of digraphs equivalently the spectra of 0 1 matrices with emphasis on the spectral radius

rational and polynomial matrix factorizations via recursive pole zero cancellation we develop a recursive algorithm for obtaining factorizations of the type r r1 r2 where all three matrices are rational and r1 is nonsingular moreover the factors r1 and r2 are such that either the poles of r1 1 and r2 are in a prescribed region of the complex plane or their zeros such factorizations cover the specific cases of coprime factorization inner outer factorization gcd extraction and many more the algorithm works on the state space or generalized state space realization of r and derives in a recursive fashion the corresponding realizations of the factors

a canonical form for pencils of matrices with applications to asymptotic linear programs abstract this paper studies asymptotic pencils of linear programs in which the constraint matrix right hand sides and objective function coefficients depend linearly on a parameter and we seek a basis that is optimal for all large or small enough values of the parameter the asymptotic linear programming formulation of discounted markov decision chains has this form as do many other problems for this problem we introduce a new canonical form for bases that facilitates computation of laurent expansions of the solutions of the resulting asymptotic linear programs and show how to implement the simplex method efficiently in this setting we show that the computational work to solve the asymptotic linear program is the product of the number of rows of the problem and the work required to solve an ordinary linear program of the same size this improves computational efficiency of the asymptotic simplex method of jeroslow 1973 and a related algorithm considered by lamond 1989 in essence this work generalizes that of miller and veinott 1969 and rothblum 1974 1975 for markov ordinary and markov branching decision chains to arbitrary linear programs

subdivision surfaces a new paradigm for thin shell finite element analysis we develop a new paradigm for thin shell finite element analysis based on the use of subdivision surfaces for i describing the geometry of the shell in its undeformed configuration and ii generating smooth interpolated displacement fields possessing bounded energy within the strict framework of the kirchhoff love theory of thin shells the particular subdivision strategy adopted here is loop s scheme with extensions such as required to account for creases and displacement boundary conditions the displacement fields obtained by subdivision are h2 and consequently have a finite kirchhoff love energy the resulting finite elements contain three nodes and element integrals are computed by a one point quadrature the displacement field of the shell is interpolated from nodal displacements only in particular no nodal rotations are used in the interpolation the interpolation scheme induced by subdivision is non local i e the displacement field over one element depend on the nodal displacements of the element nodes and all nodes of immediately neighbouring elements however the use of subdivision surfaces ensures that all the local displacement fields thus constructed combine conformingly to define one single limit surface numerical tests including the belytschko et al 10 obstacle course of benchmark problems demonstrate the high accuracy and optimal convergence of the method

a noniterative method for robustly computing the intersections between a line and a curve or surface the need to compute the intersections between a line and a high order curve or surface arises in a large number of finite element applications such intersection problems are easy to formulate but hard to solve robustly we introduce a non iterative method for computing intersections by solving a matrix singular value decomposition svd and an eigenvalue problem that is all intersection points and their parametric coordinates are determined in one shot using only standard linear algebra techniques available in most software libraries as a result the introduced technique is far more robust than the widely used newton raphson iteration or its variants the maximum size of the considered matrices depends on the polynomial degree q of the shape functions and is 2q times 3q for curves and 6 q 2 times 8 q 2 for surfaces the method has its origin in algebraic geometry and has here been considerably simplified with a view to widely used high order finite elements in addition the method is derived from a purely linear algebra perspective without resorting to algebraic geometry terminology a complete implementation is available from http bitbucket org nitro project

computing the regularization of a linear differential algebraic system abstract we study the regularization problem for linear differential algebraic systems as an improvement of former results we show that any system can be regularized by a combination of state space and input space transformations behavioral equivalence transformations and a reorganization of variables the additional state feedback which is needed in earlier publications is shown to be superfluous we provide an algorithmic procedure for the construction of the regularization and discuss computational aspects

an improved algorithm for the computation of structural invariants of a system pencil and related geometric aspects in this paper we propose a new recursive algorithm for computing the staircase form of a matrix pencil and implicitly its kronecker structure the algorithm compares favorably to existing ones in terms of elegance versatility and complexity in particular the algorithm without any modification yields the structural invariants associated with a generalized state space system and its system pencil two related geometric aspects are also discussed we show that an appropriate choice of a set of nested spaces related to the pencil leads directly to the staircase form we extend the notion of deflating subspace to the singular pencil case c 1997 elsevier science b v

finite strain viscoplasticity with nonlinear kinematic hardening phenomenological modeling and time integration abstract this article deals with a viscoplastic material model of overstress type the model is based on a multiplicative decomposition of the deformation gradient into elastic and inelastic part an additional multiplicative decomposition of inelastic part is used to describe a nonlinear kinematic hardening of armstrong frederick type two implicit time stepping methods are adopted for numerical integration of evolution equations such that the plastic incompressibility constraint is exactly satisfied the first method is based on the tensor exponential the second method is a modified euler backward method special numerical tests show that both approaches yield similar results even for finite inelastic increments the basic features of the material response predicted by the material model are illustrated with a series of numerical simulations

an improved algorithm for the computation of kronecker s canonical form of a singular pencil we give an 0 t algorithm for computing the kronecker structure of an arbitrary m x n pencil xe a the algorithm is shown to he numerically stable because only unitary transformations are used the improved speed over earlier unitary methods is due to the efficient use of condensed forms which are maintained throughout the recursions of the algorithm

introducing the concept of directly connected rheological elements by reviewing rheological models at large strains abstract rheological models are often used to exemplify the structure of phenomenological material models for this purpose different elements representing elastic viscous or plastic material behaviour are combined in parallel and series connections this article introduces a concept to material modelling within the framework of multiplicative decomposition of the deformation gradient thereby the basic idea of rheological connections is directly applied assuming the additive decomposition of the stress power relations for parallel as well as series connections are derived and the thermodynamic consistency of the concept is proved to exemplify the modelling concept an existing viscoplastic model of overstress type which is motivated by a rheological model is reviewed and reproduced to this end specific nonlinear material models representing elastic viscous and plastic material behaviour are applied in a thermodynamically consistent manner and the connection relations are evaluated finally a numerical procedure is proposed which implements the connection relations directly rather than solving the evolution equations for inelastic strains both the analytical derivation and the numerical procedure based on the connection relations yield equal results compared to standard methods which highlights the applicability of the presented concept for the development of models of multiplicative inelasticity at large strains

on the kronecker canonical form of singular mixed matrix pencils consider a linear time invariant dynamical system that can be described as f dot x t a x t b u t where a b and f are mixed matrices i e matrices having two kinds of nonzero coefficients fixed constants that account for conservation laws and independent parameters that represent physical characteristics the controllable subspace of the system is closely related to the kronecker canonical form of the mixed matrix pencil begin pmatrix a sf mid b end pmatrix under a physically meaningful assumption justified by the dimensional analysis we provide a combinatorial characterization of the sums of the minimal row column indices of the kronecker canonical form of mixed matrix pencils the characterization leads to a matroid theoretic algorithm for efficiently computing the dimension of the controllable subspace for the system with nonsingular f

on recursive computation of coprime factorizations of rational matrices abstract general computational methods based on descriptor state space realizations are proposed to compute coprime factorizations of rational matrices with minimum degree denominators the new methods rely on recursive pole dislocation techniques which allow to successively place all poles of the factors into a good region of the complex plane the resulting mcmillan degree of the denominator factor is equal to the number of poles lying in the complementary bad region and therefore is minimal the developed pole dislocation techniques are instrumental for devising numerically reliable procedures for the computation of coprime factorizations with proper and stable factors of arbitrary improper rational matrices and coprime factorizations with inner denominators implementation aspects of the proposed algorithms are discussed and illustrative examples are given

an improved toeplitz algorithm for polynomial matrix null space computation in this paper we present an improved algorithm to compute the minimal null space basis of polynomial matrices a problem which has many applications in control and systems theory this algorithm takes advantage of the block toeplitz structure of the sylvester matrix associated with the polynomial matrix the analysis of algorithmic complexity and numerical stability shows that the algorithm is reliable and can be considered as an efficient alternative to the well known pencil state space algorithms found in the literature

ab algorithm and its modifications for the spectral problems of linear pencils of matrices this paper describes and algorithm and its modifications for solving spectral problems for linear pencils of matrices both regular as well as singular

the quasi weierstras form for regular matrix pencils regular linear matrix pencils a e k n n where k q r or c and the associated differential algebraic equation dae e u x ax are studied the wong sequences of subspaces are investigate and invoked to decompose the k n into v w where any bases of the linear spaces v and wtransform the matrix pencil into the quasi weierstras form the quasi weierstras form of the matrix pencil decouples the original dae into the underlying ode and the pure dae or in other words decouples the set of initial values into the set of consistent initial values vand pure inconsistent initial values w 0 furthermore vand ware spanned by the general ized eigenvectors at the finite and infinite eigenvalues resp the quasi weierstras form is used to show how chains of generalized eigenvectors at finite and infinite eigenvalues of a e lead to the well known weierstras form so the latter can be viewed as a generalized jordan form finally it is shown how eigenvector chains constitute a basis for the solution space of e u x ax

interconnection of kronecker canonical form and special coordinate basis of multivariable linear systems this paper establishes a straightforward interconnection between the kronecker canonical form and the special coordinate basis of linear systems such an interconnection yields an alternative approach for computing the kronecker canonical form and as a by product the smith form of the system matrix of general multivariable time invariant linear systems the overall procedure involves the transformation of a given system in the state space description into the special coordinate basis which is capable of explicitly displaying all the system structural properties such as finite and infinite zero structures as well as system invertibility structures the computation of the kronecker canonical form and smith form of the system matrix is rather simple and straightforward once the given system is put under the special coordinate basis the procedure is applicable to proper systems and singular systems

on the theoretical and numerical modelling of armstrong frederick kinematic hardening in the finite strain regime abstract on the theoretical level the present paper presents a detailed comparison of recent finite strain models for armstrong frederick kinematic hardening thereby two strategies are discussed 1 chaboche type concepts considering the back stress as internal variable 2 continuum mechanical extensions of the classical rheological model using only strain like internal variables it is shown in the paper that models of the second kind can be recast in the format of anisotropic inelasticity with structure tensors second the work focuses on the algorithmic treatment of the kinematic hardening concepts presented before this problem has been tackled up to now only in the context of linearized models in contrast to isotropic finite elastoplasticity the integration cannot be carried out with respect to principal axes therefore a new integration algorithm is developed which is suitable for the anisotropic case but still retains plastic incompressibility in the case of small elastic deformation the algorithm reduces to a system of only one non linear equation and twelve linear equations in general the computational effort of the new scheme does not exceed the one of the backward euler scheme which has the disadvantage that plastic incompressibility is not fulfilled automatically several numerical examples show that the representatives of both approaches 1 and 2 yield similar results if physically reasonable material parameters are chosen

lq control of descriptor systems by cancelling structure at infinity this paper presents results concerning lq control of arbitrary descriptor systems and a numerical algorithm for achieving it the algorithm consists of two steps the first step is using the silverman algorithm orthogonal version transformation of the problem of lq control of descriptor system into a problem of lq control of a strictly proper system with singular or non singular new matrix 22 if new 22 is singular we perform the second step i e solving the lq singular control problem using again the silverman algorithm regarding the existing results on the lq singular control problem we have new results a counter example that this problem may not have a stable solution most general solvability conditions with or without stability and a new numerical algorithm based on using orthogonal matrices when stabilizability conditions are satisfied the algorithm places simultaneously stable poles in the closed loop system we show that the traditional riccati equation associated to this proble

an unfitted hp adaptive finite element method based on hierarchical b splines for interface problems of complex geometry generating finite element discretizations with direct interface parameterizations constitutes a considerable computational expense in case of complex interface geometries the paper at hand introduces a b spline finite element method which circumvents parameterization of interfaces and offers fast and easy meshing irrespective of the geometric complexity involved its core idea is the adaptive approximation of discontinuities by hierarchical grid refinement which adds several levels of local basis functions in the close vicinity of interfaces but unfitted to their exact location so that a simple regular grid of knot span elements can be maintained numerical experiments show that an hp refinement strategy which simultaneously increases the polynomial degree of the b spline basis and the levels of refinement around interfaces achieves exponential rates of convergence despite the presence of discontinuities it is also demonstrated that the hierarchical b spline fem can be used to transfer the recently introduced finite cell concept to geometrically nonlinear problems its computational performance imposition of unfitted boundary conditions and fast hierarchical grid generation are illustrated for a set of benchmark problems in one two and three dimensions and the advantages of the regular grid approach for complex geometries are demonstrated by the geometrically nonlinear simulation of a voxel based foam composite

improved upper and lower bounds for the spectral radius of digraphs let g be a digraph with n vertices and m arcs without loops and multiarcs the spectral radius r g of g is the largest eigenvalue of its adjacency matrix in this paper sharp upper and lower bounds on r g are given we show that some known bounds can be obtained from our bounds

matrix pencils and entanglement classification quantum entanglement plays a central role in quantum information processing a main objective of the theory is to classify different types of entanglement according to their interconvertibility through manipulations that do not require additional entanglement to perform while bipartite entanglement is well understood in this framework the classification of entanglements among three or more subsystems is inherently much more difficult in this paper we study pure state entanglement in systems of dimension 2 m n two states are considered equivalent if they can be reversibly converted from one to the other with a nonzero probability using only local quantum resources and classical communication slocc we introduce a connection between entanglement manipulations in these systems and the well studied theory of matrix pencils all previous attempts to study general slocc equivalence in such systems have relied on somewhat contrived techniques which fail to reveal the elegant structure of the problem that

imposing essential boundary conditions in mesh free methods imposing essential boundary conditions is a key issue in mesh free methods the mesh free interpolation does not verify the kronecker delta property and therefore the imposition of prescribed values is not as straightforward as for the finite element method the aim of this paper is to present a general overview on the existing techniques to enforce essential boundary conditions in galerkin based mesh free methods special attention is paid to the mesh free coupling with finite elements for the imposition of prescribed values and to methods based on a modification of the galerkin weak form particular examples are used to analyze and compare their performance in different situations

regularity controllability observability of an nds with descriptor form subsystems and generalized lfts abstract this paper investigates regularity controllability and observability for a networked dynamic system nds with its subsystems being described in a descriptor form and system matrices of each subsystem being represented by a generalized linear fractional transformation glft of its parameters except a well posedness condition no any other constraints are put on either parameters or connections of a subsystem based on the kronecker canonical form kcf of a matrix pencil some matrix rank based necessary and sufficient conditions are established respectively for the regularity and complete controllability observability of the nds in which the associated matrix depends affinely on both subsystem parameters and subsystem connections these conditions keep the property that all the involved numerical computations are performed on each subsystem independently which is attractive in the analysis and synthesis of a large scale nds moreover some explicit and easily checkable requirements are derived for subsystem dynamics parameters with which a completely controllable observable nds can be constructed more easily

the laurent expansion of pencils that are singular at the origin abstract this paper gives two new proofs of a theorem of langenhop on the laurent expansion of a matrix pencil that is singular at the origin the second based on a decomposition of van dooren leads to a computational algorithm

pencils of complex and real symmetric and skew matrices abstract this expository paper establishes the canonical forms under congruence for pairs of complex or real symmetric or skew matrices the treatment is in the spirit of the well known book of gantmacher on matrix theory and may be regarded as a supplement to gantmacher s chapters on pencils of matrices

zero cancellation for general rational matrix functions the problem of cancelling a specified part of the zeros of a completely general rational matrix function by multiplication with an appropriate invertible rational matrix function is investigated from different standpoints firstly the class of all factors that dislocate the zeros and feature minimal mcmillan degree are derived further necessary and sufficient existence conditions together with the construction of solutions are given when the factor fulfills additional assumptions like being j unitary or j inner either with respect to the imaginary axis or to the unit circle the main technical tool are centered realizations that deliver a sufficiently general conceptual support to cope with rational matrix functions which may be polynomial proper or improper rank deficient with arbitrary poles and zeros including at infinity a particular attention is paid to the numerically sound construction of solutions by employing at each stage unitary transformations reliable numerical algorithms for eigenvalue assignment and efficient lyapunov equation solvers

bounds on the spectral radii of digraphs in terms of walks abstract let g v e be a digraph with n vertices and m arcs without loops and multiarcs v v 1 v 2 v n denote by g the largest eigenvalue of its adjacency matrix w k i the number of k walks from vertex v i in this paper we prove that the inequalities min w p q i w q i v i v p g max w p q i w q i v i v hold for every integers p 1 q 0 if g is strongly connected then each equality holds iff w p q 1 w q 1 w p q 2 w q 2 w p q n w q n furthermore we have lim p w p q i w q i 1 p g for every integers p 1 q 0 and each vertex v i v g

subdivision stabilised immersed b spline finite elements for moving boundary flows an immersed finite element method is presented to compute flows with complex moving boundaries on a fixed cartesian grid the viscous incompressible fluid flow equations are discretized with b spline basis functions the two scale relation for b splines is used to implement an elegant and efficient technique to satisfy the lbb condition on non grid aligned fluid domains and at moving boundaries the boundary conditions are enforced with a consistent penalty method as originally proposed by nitsche in addition a special extrapolation technique is employed to prevent the loss of numerical stability in presence of arbitrarily small cut cells the versatility and accuracy of the proposed approach is demonstrated by means of convergence studies and comparisons with previous experimental and computational investigations

disturbance decoupling by behavioral feedback for linear differentialalgebraic systems we study disturbance decoupling for linear differentialalgebraic systems which are not necessarily regular compared to previous approaches where state feedback is used we use the concept of behavioral feedback which allows to study a larger class of systems we derive geometric characterizations for solvability of the disturbance decoupling problem following the classical approach exploiting the freedom in the choice of the behavioral feedback we show that whenever disturbance decoupling can be achieved by behavioral feedback we may additionally achieve autonomous zero dynamics finally we solve lebrets twenty year old open problem concerning disturbance decoupling with output uniqueness using behavioral feedback

sharp bounds for the spectral radius of digraphs abstract let g v e be a digraph with n vertices and m arcs without loops and multiarcs the spectral radius g of g is the largest eigenvalue of its adjacency matrix in this paper the following sharp bounds on g have been obtained min t i t j v i v j e g max t i t j v i v j e where g is strongly connected and t i is the average 2 outdegree of vertex v i moreover each equality holds if and only if g is average 2 outdegree regular or average 2 outdegree semiregular

numerical solution and perturbation theory for generalized lyapunov equations we discuss the numerical solution and perturbation theory for the generalized continuoustime lyapunov equation e xa a xe ig with a singular matrix e if this equation has a solution it is not unique we generalize a bartels stewart method and a hammarling method to compute a partial solution of the generalized lyapunov equation with a special right hand side a spectral condition number is introduced and perturbation bounds for such an equation are presented numerical examples are given

the generalized eigenstructure problem in linear system theory the algebraic theory of linear time invariant systems has been studied in large detail during the past few decades and numerous computational algorithms have been developed to solve problems arising in this context in this paper the numerical aspects of a certain class of such algorithms dealing with what the author calls generalized eigenstructure problems are discussed some new and or modified algorithms are presented both the nmnerical stability of the algorithms and the conditioning of the problems they solve are analyzed using numerical criteria

an explicit solution for implicit time stepping in multiplicative finite strain viscoelasticity abstract we consider the numerical treatment of one of the most popular finite strain models of the viscoelastic maxwell body this model is based on the multiplicative decomposition of the deformation gradient combined with neo hookean hyperelastic relations between stresses and elastic strains the evolution equation is six dimensional and describes an incompressible flow such that the volume changes are purely elastic for the corresponding local initial value problem a fully implicit integration procedure is considered and a simple explicit update formula is derived thus no local iterative procedure is required which makes the numerical scheme more robust and efficient the resulting integration algorithm is unconditionally stable and first order accurate the incompressibility constraint of the inelastic flow is exactly preserved a rigorous proof of the symmetry of the consistent tangent operator is provided moreover some properties of the numerical solution like invariance under the change of the reference configuration and positive energy dissipation within a time step are discussed numerical tests show that in terms of accuracy the proposed integration algorithm is equivalent to the classical implicit scheme based on the exponential mapping finally in order to check the stability of the algorithm numerically a representative initial boundary value problem involving finite viscoelastic deformations is considered a fem solution of the representative problem using msc marc is presented

squaring down with zeros cancellation in generalized systems squaring down with simultaneous zeros cancellation by series compensation of a general possibly polynomial or improper linear system is investigated all static and dynamical compensators that spotlight minimal mcmillan degree are parameterized this general result is particularized to get compensators that preserve the l 2 or l inf norm of the original system either in continuous or discrete time all results are completely general numerically sound and based on general realizations allowing for poles at infinity

spectral and inner outer factorizations through the constrained riccati equation the topic of the paper is the spectral factorization problem for a proper rational matrix function of constant rank but not necessarily maximal on the extended imaginary axis the problem is reduced to the computation of the stabilizing solution of a so called constrained riccati equation the proof of the main result suggests a schur like algorithm applied to a singular matrix pencil

polyconvexity of generalized polynomial type hyperelastic strain energy functions for near incompressibility abstract in this article we investigate several models contained in the literature in the case of near incompressibility based on invariants in terms of polyconvexity and coerciveness inequality which are sufficient to guarantee the existence of a solution these models are due to rivlin and saunders namely the generalized polynomial type elasticity and arruda and boyce the extension to near incompressibility is usually carried out by an additive decomposition of the strain energy into a volume changing and a volume preserving part where the volume changing part depends on the determinant of the deformation gradient and the volume preserving part on the invariants of the unimodular right cauchy green tensor it will be shown that the arruda boyce model satisfies the polyconvexity condition whereas the polynomial type elasticity does not therefore we propose a new class of strain energy functions depending on invariants moreover we focus our attention on the structure of further isotropic strain energy functions

parallel algorithm for solving some spectral problems of linear algebra abstract an algorithm is described for computing the deflating subspaces of a regular linear matrix pencil b a more precisely the algorithm is intended to compute the projection matrices p and i p onto the deflating subspaces of matrix pencils corresponding to the eigenvalues inside and outside the unit circle this algorithm can be considered as an orthogonal version of the matrix sign function method it possesses a quadratic convergence rate and simultaneously with the projection operators operators computes a condition number of the problem we point out the extent to which this algorithm can be parallelized applications are made to solving the riccati equation

deflation in eigenvalue assignment of descriptor systems using state feedback it is shown how deflation by unitary equivalence transformations can be used to solve the eigenvalue assignment problem for descriptor systems using state feedback the system is first transformed to a form that reveals its controllability the uncontrollable part of the system if any is then discarded and the assignments are continued with the completely controllable part of the system to give insight into the approach a mathematical method for the solution is derived without considering numerical issues using the idea of deflation it is shown how this method can be modified to derive a numerically efficient algorithm the numerical stability of the algorithm is proved and a numerical example is presented

properties of numerical algorithms related to computing controllability the numerical properties of some methods for computing controllability are used in an expository way to motivate a wider understanding of numerical computations in particular the numerical rank of a matrix the numerical stability of algorithms the sensitivity of problems and the scaling of problems are discussed a numerically stable algorithm is given for computing controllability but it is pointed out that a measure of the distance of the given system from the nearest uncontrollable system would be more useful and this appears to be an open computational problem

computation of the general j j prime lossless factorization the j j lossless factorization problem for a generalized state space system whose transfer matrix is completely general is investigated the main novelty is that we remove all restrictive hypotheses and allow for arbitrary normal rank poles and zeros on the imaginary axis or at infinity the numerically sound formulas for the solution bear the same nice expressions and striking simplicity of the inner outer factorization and may be equally well applied for the j j spectral factorization

regular article an accurate cartesian grid method for viscous incompressible flows with complex immersed boundaries a cartesian grid method has been developed for simulating two dimensional unsteady viscous incompressible flows with complex immersed boundaries a finite volume method based on a second order accurate central difference scheme is used in conjunction with a two step fractional step procedure the key aspects that need to be considered in developing such a solver are imposition of boundary conditions on the immersed boundaries and accurate discretization of the governing equation in cells that are cut by these boundaries a new interpolation procedure is presented which allows systematic development of a spatial discretization scheme that preserves the second order spatial accuracy of the underlying solver the presence of immersed boundaries alters the conditioning of the linear operators and this can slow down the iterative solution of these equations the convergence is accelerated by using a preconditioned conjugate gradient method where the preconditioner takes advantage of the structured nature of the underlying mesh the accuracy and fidelity of the solver is validated by simulating a number of canonical flows and the ability of the solver to simulate flows with very complicated immersed boundaries is demonstrated

a new look at pencils of matrix valued functions abstract matrix pencils depending on a parameter and their canonical forms under equivalence are discussed the study of matrix pencils or generalized eigenvalue problems is often motivated by applications from linear differential algebraic equations daes based on the weierstrass kronecker canonical form of the underlying matrix pencil one gets existence and uniqueness results for linear constant coefficients daes in order to study the solution behavior of linear daes with variable coefficients one has to look at new types of equivalence transformations this then leads to new canonical forms and new invariances for pencils of matrix valued functions we give a survey of recent results for square pencils and extend these results to nonsquare pencils furthermore we partially extend the results for canonical forms of hermitian pencils and give new canonicalforms there too based on these results we obtain new existence and uniqueness theorems for differential algebraic systems which generalize the classical results of weierstrass and kronecker

general matrix pencil techniques for the solution of algebraic riccati equations a unified approach we present a unified theory of matrix pencil techniques for solving both continuous and discrete time algebraic riccati equations ares under fairly general conditions on the coefficient matrices the theory applies to a large class of ares and riccati like equations arising from the singular h sup spl infin and h sup 2 control problems singular linear quadratic control the 4 block nehari problem or from singular j spectral factorizations the underlying concept is the so called proper deflating subspace of a possibly singular matrix pencil in terms of which necessary and sufficient conditions for the solvability of riccati equations are given it is shown that these conditions can be checked and the solutions computed by a numerically sound algorithm

walks and the spectral radius of graphs abstract given a graph g write g for the largest eigenvalue of its adjacency matrix g for its clique number and wk g for the number of its k walks we prove that the inequalities w q r g w q g r g g 1 g w r g hold for all r 0 and odd q 0 we also generalize a number of other bounds on g and characterize semiregular and pseudo regular graphs in spectral terms

a reduced order observer for descriptor systems abstract in this paper a reducer order observer is analyzed for so called generalized state space or descriptor systems based on the staircase form for generalized state space models a recursive algorithm is presented to construct a reduced order observer for a given observable descriptor system in the algorithm only the eigenfrequencies of the observer have to be specified

computation of structural invariants of generalized state space systems in this paper we develop an algorithm for computing the zeros of a generalized state space model described by the matrix 5 tuple e a b c d where e may be a singular matrix but det a he 0 the characterization of these zeros is based on the system matrix of the corresponding 5 tuple both the characterization and the computational algorithm are extensions of equivalent results for state space models described by the 4 tuples a b c d we also extend these results to the computation of infinite zeros and left and right minimal indices of the system matrix several non trivial numerical examples are included to illustrate the proposed results

a novel numerical method for exact model matching problem with stability in system design the exact model matching problem with stability consists of compensating a given system using a realizable control law of a specified structure in order to ensure the stability of the compensated system and achieve a target closed loop transfer function in this paper we develop a novel numerical method to verify the solvability of the problem for left invertible systems and further construct a desired solution our method has a complexity which is cubic in the state dimension of the system and the desired model and can be implemented in a numerically reliable way

nurbs enhanced finite element method nefem the development of nurbs enhanced finite element method nefem is revisited this technique allows a seamless integration of the cad boundary representation of the domain and the finite element method fem the importance of the geometrical model in finite element simulations is addressed and the benefits and potential of nefem are discussed and compared with respect to other curved finite element techniques

polynomial matrices and feedback for a polynomial matrix having full row rank for all values of the parameter number of rows less than number of columns a number of extra rows is constructed such that the completed square polynomial matrix is unimodular this construction is performed in a numerically reliable way using a deadbeat control algorithm for a generalized state space system which in turn represents the given polynomial matrix

computation of general inner outer and spectral factorizations in this paper we solve two problems in linear systems theory the computation of the inner outer and spectral factorizations of a continuous time system considered in the most general setting we show that these factorization problems rely essentially on solving for the stabilizing solution a standard algebraic riccati equation of order usually much smaller than the mcmillan degree of the transfer function matrix of the system the proposed procedures are completely general being applicable for a polynomial proper improper system whose transfer function matrix could be rank deficient and could have poles zeros on the imaginary axis or at infinity as an application we discuss the extension to the case of rational matrices of the complete orthogonal decomposition of a constant matrix numerical refinements and examples illustrating the proposed approach are discussed in detail

spectral and inner outer factorizations for discrete time systems the spectral and inner outer factorization problems are solved for discrete time systems with transfer matrices of arbitrary rank simple and explicit state space formulas expressed in terms of the stabilizing solution to the discrete time algebraic riccati system are derived the results are numerically effective since a reliable algorithm for computing such a stabilizing solution is available

using permuted graph bases in h control we present a new numerical method based on the computation of deflating subspaces for the c iteration in h control in the extended matrix pencil formulation we introduce a permuted graph representation of these subspaces which avoids the known difficulties that arise when the iteration is based on the solution of algebraic riccati equations but at the same time makes use of the special symmetry structures that are present in the problems we use this representation to perform both the deflation of spurious eigenvalues of the even pencils and the implementation of the inverse free sign iteration we show that the new method returns accurate results and is applicable in many situations where conventional methods fail

stabilizing solution to the reverse discrete time riccati equation a matrix pencil based approach abstract we derive necessary and sufficient conditions for the existence of the stabilizing solution to the reverse discrete time riccati equation a particular type of algebraic riccati equation which is related to the solution of the discrete time version of the extended two block nehari problem the conditions are expressed in terms of the left stable deflating subspace of an associated symplectic matrix pencil in particular a maximum phase spectral factorization of the popov function is obtained under very relaxed conditions imposed on the initial data it is also proved that under a restrictive additional assumption the stabilizing solution to the reverse riccati equation reduces to the antistabilizing solution to the usual discrete time riccati equation a reliable numerical algorithm for computing the stabilizing solution to the reverse riccati equation is also presented together with formulae for the solution to the extended nehari problem