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

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

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

velocity averaging kinetic formulations and regularizing effects in quasi linear pdes we prove in this paper new velocity averaging results for second order multidimensional equations of the general form l x v f x v g x v where l x v a v x b v x these results quantify the sobolev regularity of the averages v f x v v dv in terms of the nondegeneracy of the set

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

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

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

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

rogue waves for a variable coefficient kadomtsev petviashvili equation in fluid mechanics abstract under investigation in this paper is a variable coefficient kadomtsev petviashvili equation in fluid mechanics which describes the shallow water waves with the weak nonlinearity and dispersion employing the kadomtsev petviashvili hierarchy reduction we obtain the rogue wave solutions in terms of the gramian periodic cubic and s shaped line rogue waves are presented with different forms of the dispersion coefficient the second order rogue waves and multi rogue waves are also graphically discussed it is observed that only parts of the second order rogue wave approach the constant background and the other parts move to the far distance with the undiminished amplitudes the multi rogue waves describe the interaction of several first order rogue waves we plot the interactions of two periodic cubic and s shaped line rogue waves the lump wave which propagates stably in all directions is also depicted

regularity and large time behaviour of solutions of a conservation law without convexity a l aide de la methode des caracteristiques generalisees on etudie la regularite et le comportement a grand des solutions faibles admissibles d une seule loi de conservation a 1 variable d espace avec un point d inflexion

on the maximal smoothing effect for multidimensional scalar conservation laws abstract in 1994 lions perthame and tadmor conjectured an optimal smoothing effect for entropy solutions of multidimensional scalar conservation laws this effect estimated in fractional sobolev spaces is linked to the flux nonlinearity we use a new definition of a nonlinear smooth flux in order to show that the conjectured smoothing effect cannot be exceeded first one dimensional solutions are considered in fractional b v spaces then the multidimensional case is handled with a monophase solution

smoothing effect in bvφ for entropy solutions of scalar conservation laws abstract this paper deals with a sharp smoothing effect for entropy solutions of one dimensional scalar conservation laws with a degenerate convex flux we briefly explain why degenerate fluxes are related with the optimal smoothing effect conjectured by lions perthame tadmor for entropy solutions of multidimensional conservation laws it turns out that generalized spaces of bounded variation b v are particularly suitable better than sobolev spaces to quantify the regularizing effect and to obtain traces as in bv the function in question is linked to the degeneracy of the flux up to the present the lax ole nik formula has provided optimal results for a uniformly convex flux this formula is validated in this paper for the more general class of c 1 strictly convex fluxes which contains degenerate convex fluxes and enables the b v smoothing effect in this class we give a complete proof that for a c 1 strictly convex flux the lax ole nik formula provides the unique entropy solution namely the kruzhkov solution

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

strong traces for solutions of multidimensional scalar conservation laws in this paper we consider multidimensional scalar conservation laws without bv estimates defined in a subset d we show that with a non degeneracy hypothesis on the flux we can define a strong notion of trace at the boundary of reached by l 1 convergence

structure of entropy solutions for multi dimensional scalar conservation laws an entropy solution u of a multi dimensional scalar conservation law is not necessarily in bv even if the conservation law is genuinely nonlinear we show that u nevertheless has the structure of a bv function in the sense that the shock location is codimension one rectifiable this result highlights the regularizing effect of genuine nonlinearity in a qualitative way it is based on the locally finite rate of entropy dissipation the proof relies on the geometric classification of blow ups in the framework of the kinetic formulation

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

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

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

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

semi rational solutions for the 3 1 dimensional kadomtsev petviashvili equation in a plasma or fluid abstract in this paper we investigate the 3 1 dimensional kadomtsev petviashvili equation in a plasma or fluid for the amplitude of the electrostatic wave potential in the plasma or shallow water wave in the fluid via the kadomtsev petviashvili hierarchy reduction we obtain the semi rational solutions in determinant form for such an equation interactions between the first order lump or rogue wave and soliton are illustrated we find that the lump arises and then separates from the soliton on the x y and x z planes and that the rogue wave possesses a line profile and arises from the soliton or constant background on the y z plane where x y and z are the scaled spatial coordinates interactions between the two lumps or rogue waves and two solitons are presented interactions between the second order lump or rogue wave and one soliton are also presented

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

large time behavior and homogenization of solutions of two dimensional conservation laws we study the large time behavior of solutions of scalar conservation laws in one and two space dimensions with periodic initial data under a very weak nonlinearity condition we prove that the solutions converge to constants as time goes to infinity even in one space dimension our results improve the earlier ones since we only require the fluxes to be nonlinear in a neighborhood of the mean value of the initial data we then use these results to study the homogenization problem for scalar conservation laws with oscillatory initial data

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

validity of nonlinear geometric optics for entropy solutions of multidimensional scalar conservation laws nonlinear geometric optics with various frequencies for entropy so lutions only in l 1 of multidimensional scalar conservation laws is analyzed a new approach to validate nonlinear geometric optics is developed via entropy dissipation through scaling compactness homogenization and l 1 stability new multidimensional features are recognized especially including nonlinear propagations of oscillations with high frequencies the validity of nonlinear geometric optics for entropy solutions in l 1 of multidimensional scalar con servation laws is justified

classification of arbitrary dimensional multipartite pure states under stochastic local operations and classical communication using the rank of coefficient matrix we study multipartite entanglement under stochastic local operations and classical communication slocc and propose the entanglement classification under slocc for arbitrary dimensional multipartite n qudit pure states via the rank of coefficient matrix together with the permutation of qudits the ranks of the coefficient matrices have been proved to be entanglement monotones the entanglement classification of the 2 2 2 4 system is discussed in terms of the generalized method and 22 different slocc families are found

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

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

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

mobius transformations of matrix polynomials we discuss mobius transformations for general matrix polynomials over arbitrary fields analyzing their influence on regularity rank determinant constructs such as compound matrices and on structural features including sparsity and symmetry results on the preservation of spectral information contained in elementary divisors partial multiplicity sequences invariant pairs and minimal indices are presented the effect on canonical forms such as smith forms and local smith forms on relationships of strict equivalence and spectral equivalence and on the property of being a linearization or quadratification are investigated we show that many important transformations are special instances of mobius transformations and analyze a mobius connection between alternating and palindromic matrix polynomials finally the use of mobius transformations in solving polynomial inverse eigenproblems is illustrated

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

entanglement of pure states for a single copy an optimal local conversion strategy between any two pure states of a bipartite system is presented it is optimal in that the probability of success is the largest achievable if the parties which share the system and which can communicate classically are only allowed to act locally on it the study of optimal local conversions sheds some light on the entanglement of a single copy of a pure state we propose a quantification of such an entanglement by means of a finite minimal set of new measures from which the optimal probability of conversion follows

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

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

description of rank four entangled states of two qutrits having positive partial transpose it is known that some two qutrit entangled states of rank 4 with positive partial transpose can be built from the unextendible product bases upb c h bennett d p divincenzo t mor p w shor j a smolin and b m terhal phys rev lett 82 5385 1999 we show that this fact is indeed universal namely all such states can be constructed from upb as conjectured recently by leinaas myrheim and sollid we also classify the five dimensional subspaces of two qutrits which contain only finitely many product states up to scalar multiple and in particular those spanned by an upb

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

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

resonant one dimensional nonlinear geometric optics abstract in this paper we study the existence and resonant interaction of oscillatory wave trains in one space dimension giving a rigorous proof of the validity of the corresponding expansions of weakly nonlinear optics we consider both semilinear and quasilinear systems the latter before shock formation some important features of the study are the following 1 we prove the existence of families of exact solutions which have asymptotic expansions governed by weakly nonlinear optics equations with variable coefficients nonconstant background fields and nonlinear phases are permitted our weak transversality hypotheses allow us to justify expansions where even a formal theory did not exist before 2 we make a detailed study of resonances the geometry associated with such resonances is related to the theory of planar webs 3 we study the smoothness of the profiles their regularity is ruled by a sum law analogous to that describing the propagation of singularities in one dimension 4 the expansions are justified up to the breakdown of the profiles which coincides with a suitably defined breakdown for exact solutions

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

a symbolic computation approach to constructing rogue waves with a controllable center in the nonlinear systems abstract a symbolic computation approach to constructing higher order rogue waves with a controllable center of the nonlinear systems is presented making use of their hirota bilinear forms as some examples it turns out that some higher order rogue wave solutions of the kadomtsev petviashvili kp type equations in 3 1 and 2 1 dimensions are obtained some features of controllable center of rogue waves are graphically discussed

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

total oscillation diminishing property for scalar conservation laws we prove a bv estimate for scalar conservation laws that generalizes the classical total variation diminishing property in fact for any lipschitz continuous monotone we have that u tv is nonincreasing in time we call this property total oscillation diminishing because it is in contradiction with the oscillations observed recently in some numerical computations based on tvd schemes we also show that semi discrete total variation diminishing finite volume schemes are tod and that the fully discrete godunov scheme is tod

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