successive iteration and positive pseudo symmetric solutions for a three point second order p laplacian boundary value problems in this paper we study the existence of positive pseudo symmetric solutions for a three point second order p laplacian boundary value problems with dependence on the first order derivative by applying a monotone iterative method

the inverse eigenvalue problem for nonnegative matrices abstract let a be a nonnegative matrix with spectrum 1 2 m and b be a nonnegative matrix with spectrum 1 2 n where 1 is the perron eigenvalue of b furthermore let a maximal diagonal element of a be greater than or equal to 1 in the article we construct a nonnegative matrix c with spectrum 1 2 m 2 n this construction enables us to obtain several results on how to determine new realizable lists from known realizable lists

nonnegative realizability with jordan structure abstract a general method is given for merging blocks in the jordan canonical form of a nonnegative matrix as a consequence results more general than any prior ones are given for the universal realizability of spectra that is spectra which are realizable by a nonnegative matrix for each possible jordan canonical form allowed by the spectrum in particular we generalize a classical result due to minc regarding positive diagonalizable matrices for example any spectrum that is diagonalizably realizable by a nonnegative matrix with mostly positive off diagonal entries is universally realizable

a multistage representation of the wiener filter based on orthogonal projections the wiener filter is analyzed for stationary complex gaussian signals from an information theoretic point of view a dual port analysis of the wiener filter leads to a decomposition based on orthogonal projections and results in a new multistage method for implementing the wiener filter using a nested chain of scalar wiener filters this new representation of the wiener filter provides the capability to perform an information theoretic analysis of previous basis dependent reduced rank wiener filters this analysis demonstrates that the cross spectral metric is optimal in the sense that it maximizes mutual information between the observed and desired processes a new reduced rank wiener filter is developed based on this new structure which evolves a basis using successive projections of the desired signal onto orthogonal lower dimensional subspaces the performance is evaluated using a comparative computer analysis model and it is demonstrated that the low complexity multistage reduced rank wiener filter is capable of outperforming the more complex eigendecomposition based methods

negativity compensation in the nonnegative inverse eigenvalue problem abstract if a set of complex numbers can be partitioned as 1 s in such a way that each i is realized as the spectrum of a nonnegative matrix say a i then is trivially realized as the spectrum of the nonnegative matrix a a i in linear algebra appl 369 2003 169 it was shown that in some cases a real set can be realized even if some of the i are not realizable themselves here we systematize and extend these results in particular allowing the sets to be complex the leading idea is that one can associate to any nonrealizable set a certain negativity n and to any realizable set a certain positivity m then under appropriate conditions if m n we can conclude that is the spectrum of a nonnegative matrix additionally we prove a complex generalization of suleimanova s theorem

estimation of the mean of a multivariate normal distribution estimation of the means of independent normal random variables is considered using sum of squared errors as loss an unbiased estimate of risk is obtained for an arbitrary estimate and certain special classes of estimates are then discussed the results are applied to smoothing by use of moving averages and to trimmed analogs of the james stein estimate a suggestion is made for calculating approximate confidence sets for the mean vector centered at an arbitrary estimate

nonnegative matrices with prescribed spectrum and elementary divisors abstract in this paper we give new sufficient conditions for the existence and construction of nonnegative matrices with prescribed elementary divisors which drastically improve and contain some of the previous known conditions we also show how to perturb complex eigenvalues of a nonnegative matrix while keeping its nonnegativity these results allow us under certain conditions to easily decide if a given list is realizable with prescribed elementary divisors

realizing suleĭmanova spectra via permutative matrices ii abstract in this work the real nonnegative inverse eigenvalue problem is solved for a particular class of permutative matrix the necessary and sufficient condition there is also shown to be sufficient for the symmetric nonnegative inverse eigenvalue problem a result due to johnson and paparella 2016 8 is extended to include normalized lists that satisfy the new sufficient condition

singular nonlinear boundary value problems for second order ordinary differential equations abstract the boundary value problem y f x y 0 y 0 y 0 0 y 1 y 1 0 is studied under conditions which are modeled on the problem y a x y p 0y 0 y 1 0 or y 0 y 1 0 which occurs in a number of applications the technical arguments involve properties of solutions i e concavity and the use of iterative techniques a new fixed point theorem for cones for decreasing mappings is proved and used it is of interest in its own right since most such theorems are for monotone increasing mappings

a map of sufficient conditions for the real nonnegative inverse eigenvalue problem abstract the real nonnegative inverse eigenvalue problem rniep is the problem of determining necessary and sufficient conditions for a list of real numbers to be the spectrum of an entrywise nonnegative matrix a number of sufficient conditions for the existence of such a matrix are known in this paper in order to construct a map of sufficient conditions we compare these conditions and establish inclusion relations or independency relations between them

a unified view on compensation criteria in the real nonnegative inverse eigenvalue problem a connection is established between the problem of characterizing all possible real spectra of entrywise nonnegative matrices the so called real nonnegative inverse eigenvalue problem and a combinatorial process consisting in repeated application of three basic manipulations on sets of real numbers given realizable sets i e sets which are spectra of some nonnegative matrix each of these three elementary transformations constructs a new realizable set this defines a special kind of realizability called c realizability and this is closely related to the idea of compensation after observing that the set of all c realizable sets is a strict subset of the set of realizable ones we show that it strictly includes in particular all sets satisfying several previously known sufficient realizability conditions in the literature furthermore the proofs of these conditions become much simpler when approached from this new point of view

universal realizability of spectra with two positive eigenvalues abstract a list of eigenvalues is said to be realizable if it is the spectrum of a nonnegative matrix diagonalizably realizable dr if it is the spectrum of a diagonalizable nonnegative matrix and universally realizable ur if there is a nonnegative matrix with this spectrum and any possible jordan canonical form allowed by the spectrum the nonnegative inverse eigenvalue problem niep asks which lists are realizable it is known that there exist spectra that are realizable but not dr we raise the question of whether dr implies ur this is known in a few cases including n 4 nonnegative spectra and suleimanova spectra we add some new classes of spectra that are ur

the symmetric nonnegative inverse eigenvalue problem for 5 5 matrices abstract the symmetric nonnegative inverse eigenvalue problem sniep asks when a list 1 2 n of n real numbers is the spectrum of an n n symmetric nonnegative matrix this problem is completely solved only for n 4 our main goal here is to contribute to the solution of sniep for n 5 we also give a sufficient condition for a list to be realized as the spectrum of a symmetric positive matrix

the nonnegative inverse eigenvalue problem from the coefficients of the characteristic polynomial ebl digraphs the nonnegative inverse eigenvalue problem niep is given a family of complex numbers 1 n find necessary and sufficient conditions for the existence of a nonnegative matrix a of order n with spectrum loewy and london r loewy d london a note on the inverse eigenvalue problems for nonnegative matrices linear and multilinear algebra 6 1978 83 90 resolved it for n 3 and for n 4 when the spectrum is real in our way of handling the niep we focus our attention on the coefficients of the characteristic polynomial of a thus the niep that we consider is given k1 k2 kn real numbers find necessary and sufficient conditions for the existence of a nonnegative matrix a of order n with characteristic polynomial xn k1xn 1 k2xn 2 kn the coefficients of the characteristic polynomial are closely related to the cyclic structure of the weighted digraph with adjacency matrix a we introduce a special type of digraph structure that we shall call ebl in which this relation is specially simple we give some results that show the interest of ebl structures we completely solve the niep from the coefficients of the characteristic polynomial for n 4 we also solve a special case of the niep for n 2p 1 with k1 kp 1 0 and p 2

the geometry of weighted low rank approximations the low rank approximation problem is to approximate optimally with respect to some norm a matrix by one of the same dimension but smaller rank it is known that under the frobenius norm the best low rank approximation can be found by using the singular value decomposition svd although this is no longer true under weighted norms in general it is demonstrated here that the weighted low rank approximation problem can be solved by finding the subspace that minimizes a particular cost function a number of advantages of this parameterization over the traditional parameterization are elucidated finding the minimizing subspace is equivalent to minimizing a cost function on the grassmann manifold a general framework for constructing optimization algorithms on manifolds is presented and it is shown that existing algorithms in the literature are special cases of this framework within this framework two novel algorithms a steepest descent algorithm and a newton like algorithm are derived for solving the weighted low rank approximation problem they are compared with other algorithms for low rank approximation as well as with other algorithms for minimizing a cost function on a grassmann manifold

analysis of blowup for a nonlinear degenerate parabolic equation in this paper the nonlinear degenerate parabolic equation ut u u u subject to dirichlet boundary conditions is studied the finite time blowup result together with an estimate of the blowup time is found the blowup set with positive measure and the asymptotic behavior of solution near the blowup time are analyzed in some detail via the similarity solutions

elgenvalues of nonnegative matrices abstract in a partial continuation of work by fiedler some spectral properties of symmetric nonnegative matrices are extended to general nonnegative matrices

existence and construction of nonnegative matrices with prescribed spectrum abstract we consider the following inverse spectrum problem for nonnegative matrices given a set of real numbers 1 2 n find necessary and sufficient conditions for the existence of an n n nonnegative matrix a with spectrum in particular by the use of a relevant theorem of brauer we obtain new simple sufficient conditions for the problem to have a solution moreover we can always construct a solution matrix which is nonnegative generalized stochastic

detecting anomalous deviations from standard maritime routes using the ornstein uhlenbeck process a novel anomaly detection procedure based on the ornstein uhlenbeck ou mean reverting stochastic process is presented the considered anomaly is a vessel that deviates from a planned route changing its nominal velocity boldsymbol v 0 in order to hide this behavior the vessel switches off its automatic identification system ais device for a time t and then tries to revert to the previous nominal velocity boldsymbol v 0 the decision that has to be made is declaring that a deviation either happened or not relying only upon two consecutive ais contacts furthermore the extension to the scenario in which multiple contacts e g radar are available during the time period t is also considered a proper statistical hypothesis testing procedure that builds on the changes in the ou process long term velocity parameter boldsymbol v 0 of the vessel is the core of the proposed approach and enables the solution of the anomaly detection problem closed analytical forms are provided for the detection and false alarm probabilities of the hypothesis test

nonnegative realization of spectra having negative real parts abstract the nonnegative inverse eigenvalue problem niep is the problem of determining necessary and sufficient conditions for a list of complex numbers to be the spectrum of a nonnegative matrix in this paper the problem is completely solved in the case when all numbers in the given list except for one the perron eigenvalue have real parts smaller than or equal to zero

realizability criterion for the symmetric nonnegative inverse eigenvalue problem abstract let 1 2 n a set of real numbers the real nonnegative inverse eigenvalue problem rniep is the problem of determining necessary and sufficient conditions in order that be the spectrum of an entrywise nonnegative n n matrix if there exists a nonnegative matrix a with spectrum we say that is realized by a many realizability criteria for the existence of such a matrix a are known this paper shows that a realizability criterion given by the author which contains both kellogg s realizability criterion and borobia s realizability criterion is sufficient for the existence of an n n symmetric nonnegative matrix with prescribed spectrum

on nonnegative matrices with prescribed eigenvalues and diagonal entries abstract we consider the problem of the existence and construction of nonnegative matrices with prescribed spectrum and diagonal entries necessary and sufficient conditions have been obtained for n 3 by perfect and fiedler in the cases nonnegative and nonnegative symmetric respectively for n 4 they obtained sufficient conditions many partial results about the problem have been published by several authors mainly by smigoc this is a long standing unsolved inverse problem but also necessary to apply a perturbation result due to r rado which has played an important role in the study of nonnegative inverse eigenvalue and inverse elementary divisors problems distinct versions of rado s result have been also obtained for certain structured matrices to apply rado s result and its different versions we need to guarantee the existence of an r r r n nonnegative structured matrix with prescribed spectrum and diagonal entries this is an important motivation for this work here we prove new sufficient conditions for n 4 which extend and strictly contain the perfect and fiedler conditions our results generate an algorithmic procedure to construct a solution matrix

a characterization of trace zero nonnegative 5 5 matrices let 1 2 3 4 5 be a list of complex numbers with 1 2 3 4 5 0 necessary and sufficient conditions for the existence of an entry wise nonnegative 5 5 matrix a with spectrum are presented

existence and construction of nonnegative matrices with complex spectrum abstract the following inverse spectrum problem for nonnegative matrices is considered given a set of complex numbers 1 2 n find necessary and sufficient conditions for the existence of an n n nonnegative matrix a with spectrum our work is motivated by a relevant theoretical result of guo wuwen linear algebra appl 266 1997 261 theorem 2 1 there exists a real parameter 0 max 2 j n j such that the problem has a solution if and only if 1 0 in particular we discuss how to compute 0 and the solution matrix a for certain class of matrices a sufficient condition for the problem to have a solution is also derived

nonnegative matrices with prescribed extremal singular values we consider the problem of constructing nonnegative matrices with prescribed extremal singular values in particular given 2n 1 real numbers s 1 j and s j j j 1 n we construct an nxn nonnegative bidiagonal matrix b and an nxn nonnegative semi bordered diagonal matrix c such that s 1 j and s j j are respectively the minimal and the maximal singular values of certain submatrices b j and c j of b and c respectively by using a singular value perturbation result we also construct an nxn nonnegative matrix with prescribed singular values s 1 s n

an inverse eigenvalue problem for the finite element model of a vibrating rod an inverse eigenvalue problem for the finite element model of a longitudinally vibrating rod whose one end is fixed and the other end is supported on a spring is considered it is known that the mass and stiffness matrices are both tridiagonal for the finite element model of the rod based on linear shape functions it is shown that the cross section areas can be determined from the spectrum of the rod the inverse vibration problem can be recast into an inverse eigenvalue problem of a special jacobi matrix the necessary and sufficient conditions for the construction of a physically realizable rod with positive cross section areas are established a numerical method is presented and an illustrative example is given

perron spectratopes and the real nonnegative inverse eigenvalue problem abstract call an n by n invertible matrix s a perron similarity if there is a real non scalar diagonal matrix d such that s d s 1 is entrywise nonnegative we give two characterizations of perron similarities and study the polyhedra c s x r n s d x s 1 0 d x diag x and p s x c s x 1 1 which we call the perron spectracone and perron spectratope respectively the set of all normalized real spectra of diagonalizable nonnegative matrices may be covered by perron spectratopes so that enumerating them is of interest the perron spectracone and spectratope of hadamard matrices are of particular interest and tend to have large volume for the canonical hadamard matrix as well as other matrices the perron spectratope coincides with the convex hull of its rows in addition we provide a constructive version of a result due to fiedler 9 theorem 2 4 for hadamard orders and a constructive version of the boyle handelman theorem 2 theorem 5 1 for sule manova spectra

constructing symmetric nonnegative matrices via the fast fourier transform abstract we derive an algorithm based on the fast fourier transform to construct a real symmetric matrix s with eigenvalues 1 2 n with eigenvector e 1 1 1 t belonging to the eigenvalue 1 we find simple conditions on the eigenvalues such that the algorithm constructs an irreducible matrix s 1 e where e is a symmetric doubly stochastic matrix

existence of positive solutions to some singular and nonsingular second order boundary value problems abstract the topological transversality theorem is employed to study existence of solutions to a variety of singular and nonsingular second order boundary value problems of the form y f t y y 0 0 t t 0 t 1 y 0 and or y 0 the principal tools are the arzela ascoli theorem essential maps and a priori bounds on solutions

realizable lists via the spectra of block matrices abstract in this paper we present spectral results for matrices partitioned into higher order blocks where not all blocks are necessarily square using these results sufficient conditions on a given list to be the list of eigenvalues of a nonnegative matrix are obtained and the corresponding matrix is constructed in particular spectral results for symmetric matrices are derived a result on guo perturbations for permutative matrices on given lists is generalized

efficient computational methods for singular free boundary problems using smoothing variable substitutions we study a class of singular free boundary problems for the degenerate m laplacian taking into account the behavior of the solution in the neighborhood of the singular points a variable substitution is introduced which makes the solution smooth in all the domain then a standard finite difference scheme is used to discretize the problem the numerical results suggest that in this way the second order convergence of the finite difference scheme is recovered in spite of the singularities

realizable lists via the spectra of structured matrices abstract a square matrix of order n with n 2 is called a permutative matrix or permutative when all its rows up to the first one are permutations of precisely its first row in this paper the spectra of a class of permutative matrices are studied in particular spectral results for matrices partitioned into 2 by 2 symmetric blocks are presented and using these results sufficient conditions on a given list to be the list of eigenvalues of a nonnegative permutative matrix are obtained and the corresponding permutative matrices are constructed guo perturbations on given lists are exhibited

on the bisymmetric nonnegative inverse eigenvalue problem abstract the problem of finding conditions for a list of n complex numbers to be the eigenvalues of an n n nonnegative matrix is called the nonnegative inverse eigenvalue problem niep the sniep bniep is the niep when the desired matrices are symmetric bisymmetric recently some sufficient conditions for the bniep are given by julio and soto in 6 in this article we study the bniep for n 4 and prove that the bniep and sniep are different for n 6 then we give some sufficient conditions for the bniep and for the niep for normal centrosymmetric matrices related to the sufficient conditions of julio and soto and we also provide certain sufficient conditions for the bniep analogous to the sufficient conditions for the niep given by borobia in 1 finally we give sufficient conditions for the bniep when the prescribed diagonal entries are required

analytical numerical investigation of a singular boundary value problem for a generalized emden fowler equation in this paper we are concerned about a singular boundary value problem for a quasilinear second order ordinary differential equation involving the one dimensional p laplacian asymptotic expansions of the one parameter families of solutions satisfying the prescribed boundary conditions are obtained in the neighborhood of the singular points and this enables us to compute numerical solutions using stable shooting methods

on the universal realizability problem abstract we say that a list 1 2 n of complex numbers is realizable if it is the spectrum of an entrywise nonnegative matrix a we say that is universally realizable ur if is realizable for each possible jordan canonical form allowed by the universal realizability problem of spectra urp has been solved for certain kind of real and complex spectra mainly spectra in the left half plane in this paper we look for extending the kind of spectra that are ur by given new sufficient conditions for the urp to have a solution in particular we show that some realizability criteria for the real and symmetric nonnegative inverse eigenvalue problem are realizability criteria for the urp as well

on the nonnegative eigenvalue problem abstract 1 1 n is the spectrum of a stochastic matrix of order n 1 if and only if there exists some real matrix b of order n with spectrum 1 n and some n simplex s r n containing the origin such that bs s this result appears implicitly in ciarlet s work and it provides us with a geometrical tool to obtain sufficient conditions for the nonnegative eigenvalue problem we employ it here to generalize the sufficient conditions given by kellogg

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

bi iteration svd subspace tracking algorithms we present a class of fast subspace tracking algorithms that arise from a straightforward extension of bauer s 1957 classical bi iteration to the sequential processing case the bi iteration concept has an unexpected potential in subspace tracking our new bi svd subspace trackers are well structured and show excellent convergence properties they outperform the tqr svd subspace tracking algorithm detailed comparisons confirm our claims an application to rank and data adaptive signal reconstruction is also discussed

an algorithm for constructing nonnegative matrices with prescribed real eigenvalues provided with the real spectrum this paper presents a numerical procedure based on the induction principle to solve two types of inverse eigenvalue problems one for nonnegative matrices and another for symmetric nonnegative matrices as an immediate application our approach can offer not only the sufficient condition to solve inverse eigenvalue problems for nonnegative or symmetric nonnegative matrices but also a numerical way to solve inverse eigenvalue problems for stochastic matrices numerical examples are presented to show the capacity of our method

the nonnegative inverse eigenvalue problem abstract let 1 n be a list of complex numbers the nonnegative inverse eigenvalue problem niep is the problem of determining necessary and sufficient conditions in order that be the spectrum of an entrywise nonnegative n n matrix our purpose is to give an overview of the niep its history modern results and subproblems with particular emphasis on symmetric realizing matrices a substantial bibliography is included

numerical solution of a class of singular free boundary problems involving the m laplace operator for a class of singular free boundary problems with applications in electromagnetism and plasma physics an analytical numerical approach is proposed based on the asymptotic expansion of the solution in the neighborhood of the singular points this approach was already used to approximate the solution of certain classes of singular boundary value problems on bounded lima and morgado 2009 14 and unbounded domains konyukhova et al 2008 12 here one parameter families of solutions of suitable singular cauchy problems describing the behavior of the solution at the singularities are derived and based on these families numerical methods for the approximation of the solution of the free boundary problems are constructed

existence and iteration of positive solutions for some p laplacian boundary value problems abstract this paper deals with the existence and iteration of positive solutions for the following p laplacian differential equation p u t q t f t u t u t 0 t 0 1 subject to one of the following boundary conditions p u 0 p u 0 0 p u 1 p u 1 0 or u 0 g 1 u 0 0 u 1 g 2 u 1 0 the main tool is the monotone iterative technique we obtain not only the existence of positive solutions for the problems but also establish iterative schemes for approximating the solutions

existence uniqueness and nondegeneracy of positive solutions of semilinear elliptic equations we study positive solutions of the dirichlet problem a u x f u x 0 x d u x o x e ad where d is an n ball we find necessary and sufficient conditions for solutions to be nondegenerate we also give some new existence and uniqueness theorems in this paper we study positive solutions of the dirichlet problem au x f u x o x f2

on nonnegative matrices similar to positive matrices abstract let nn denote the set of those 1 2 n c n such that there exists a nonnegative matrix with perron root equal to one and spectrum 1 2 n we prove that nn is star shaped with respect to 1 0 0 and that 1 2 n n n is on the boundary of nn if and only if 1 2 n is not the spectrum of any positive matrix as a consequence attention is given to the problem of determining which nonnegative matrices are similar to positive ones more precisely we address the question of which pattern matrices p satisfy that any nonnegative matrix with pattern p is similar to a positive matrix some partial results are obtained among them that any irreducible nonnegative matrix with a positive line is similar to a positive matrix which allow us to give a complete solution to the case of 3 by 3 matrices

isospectral flow method for nonnegative inverse eigenvalue problem with prescribed structure the nonnegative inverse eigenvalue problem is that given a family of complex numbers l l 1 l n find a nonnegative matrix of order n with spectrum l this problem is difficult and remains unsolved partially in this paper we focus on its generalization that the reconstructed nonnegative matrices should have some prescribed entries it is easy to see that this new problem will come back to the common nonnegative inverse eigenvalue problem if there is no constraint of the locations of entries a numerical isospectral flow method which is developed by hybridizing the optimization theory and steepest descent method is used to study the reconstruction moreover an error estimate of the numerical iteration for ordinary differential equations on the matrix manifold is presented after that a numerical method for the nonnegative symmetric inverse eigenvalue problem with prescribed entries and its error estimate are considered finally the approaches are verified by the numerical test results

the real nonnegative inverse eigenvalue problem is np hard abstract a list of complex numbers is realizable if it is the spectrum of a nonnegative matrix in 1949 suleimanova posed the nonnegative inverse eigenvalue problem niep the problem of determining which lists of complex numbers are realizable the version for reals of the niep rniep asks for realizable lists of real numbers in the literature there are many sufficient conditions or criteria for lists of real numbers to be realizable we will present an unified account of these criteria then we will see that the decision problem associated to the rniep is np hard and we will study the complexity for the decision problems associated to known criteria

on the comparison of some realizability criteria for the real nonnegative inverse eigenvalue problem abstract a result by brauer shows how to modify one single eigenvalue of a matrix via a rank one perturbation without changing any of the remaining eigenvalues this together with the properties of real matrices with constant row sums was exploited by the authors in a previous work in connection with the nonnegative inverse eigenvalue problem obtaining conditions which are sufficient for the existence of an entrywise nonnegative matrix with prescribed spectrum in this work we make use of brauer s theorem again to show that most of the previous results giving sufficient conditions for the real nonnegative inverse eigenvalue problem can be derived by using brauer s theorem moreover the technique is constructive and there is an algorithmic procedure to construct a matrix realizing the spectrum in particular we show that if either kellogg s realizability criterion or borobia s realizability criterion is satisfied then soto s realizability criterion is also satisfied none of the converses are true thus the condition given by soto appears to be the most general sufficient condition so far for the real nonnegative inverse eigenvalue problem

data adaptive rank shaping methods for solving least squares problems there are two types of problems in the theory of least squares signal processing parameter estimation and signal extraction parameter estimation is called inversion and signal extraction is called filtering in this paper we present a unified theory of rank shaping for solving overdetermined and underdetermined versions of these problems we develop several data dependent rank shaping methods and evaluate their performance our key result is a data adaptive wiener filter that automatically adjusts its gains to accommodate realizations that are a priori unlikely the adaptive filter dramatically outperforms the wiener filter on a typical realizations and just slightly under performs it on typical realizations this is the most one can hope for in a data adaptive filter

various 3 3 nonnegative matrices with prescribed eigenvalues and diagonal entries abstract in this paper we answer the various forms of nonnegative inverse eigenvalue problems with prescribed diagonal entries for order three real or complex general matrices symmetric stochastic matrices and real or complex doubly stochastic matrices we include the known cases the symmetric matrices and real or complex stochastic matrices to compare the other results and for completeness in addition for a given list of eigenvalues we compute the exact range for the largest value of the diagonal entries of the various nonnegative matrices

boundary element method for a free third boundary problem modeling tumor growth with spectral accuracy abstract by boundary element method we present a numerical iterative process for solving a free third boundary problem modeling tumor growth with spectral accuracy the piecewise quadratic curves are fitted to maintain local smoothness of the boundary at every node the double layer and single layer potentials with weakly singular kernels are evaluated with spectral accuracy the method of characteristics is employed to transform interfacial velocity pde into discrete odes the numerical integral formula for weakly singular operator with logarithmic singularity is deduced and the convergence and error are presented the nonradially symmetric solutions of the free boundary problem on a perturbed boundary are provided to test the accuracy and effectiveness of the numerical method

connecting sufficient conditions for the symmetric nonnegative inverse eigenvalue problem abstract we say that a list of real numbers is symmetrically realisable if it is the spectrum of some entrywise nonnegative symmetric matrix the symmetric nonnegative inverse eigenvalue problem sniep is the problem of characterising all symmetrically realisable lists in this paper we present a recursive method for constructing symmetrically realisable lists the properties of the realisable family we obtain allow us to make several novel connections between a number of sufficient conditions developed over forty years starting with the work of fiedler in 1974 we show that essentially all previously known sufficient conditions are either contained in or equivalent to the family we are introducing

a note on methods for constructing distance matrices and the inverse eigenvalue problem abstract in this paper a symmetric nonnegative matrix with zero diagonal and given spectrum where exactly one of the eigenvalues is positive is constructed this solves the symmetric nonnegative eigenvalue problem sniep for such a spectrum the construction is based on the idea from the paper hayden reams wells methods for constructing distance matrices and the inverse eigenvalue problem some results of this paper are enhanced the construction is applied for the solution of the inverse eigenvalue problem for euclidean distance matrices under some assumptions on the eigenvalues

solving inverse eigenvalue problems via householder and rank one matrices abstract a brief and practical algorithm is introduced to solve symmetric inverse eigenvalue problems which we call hrou algorithm the algorithm is based on householder transformations and rank one updating we give some basic properties and the computational amount and develop sensitivity analysis of hrou algorithm furthermore we develop hrou algorithm into a multi level and adaptive one named mlahrou to solve symmetric nonnegative inverse eigenvalue problems new sufficient conditions to ensure symmetric nonnegative matrices and symmetric m matrices are given many numerical examples are given to verify our theory compare with existing results and show the efficiency of our algorithms

on the spectra of some g circulant matrices and applications to nonnegative inverse eigenvalue problem abstract a g circulant matrix a is defined as a matrix of order n where the elements of each row of a are identical to those of the previous row but are moved g positions to the right and wrapped around using number theory certain spectra of g circulant real matrices are given explicitly the obtained results are applied to nonnegative inverse eigenvalue problem to construct nonnegative g circulant matrices with given appropriated spectrum additionally some g circulant matrices are reconstructed from its main diagonal entries

more comments on c p we discuss the interpretation of c p plots and show how they can be calibrated in several ways we comment on the practice of using the display as a basis for formal selection of a subset regression model and extend the range of application of the device to encompass arbitrary linear estimates of the regression coefficients for example ridge estimates

spectra of principal submatrices of nonnegative matrices abstract let a be an n n nonnegative matrix with the spectrum 1 2 n and let a 1 be an m m principal submatrix of a with the spectrum 1 2 m in this paper we present some cases where the realizability of 1 2 m 1 2 s implies the realizability of 1 2 n 1 2 s and consider the question whether this holds in general in particular we show that the list 1 2 n 1 2 m is realizable

mv pure estimator minimum variance pseudo unbiased reduced rank estimator for linearly constrained ill conditioned inverse problems this paper proposes a novel estimator named minimum variance pseudo unbiased reduced rank estimator mv pure for the linear regression model designed specially for the case where the model matrix is ill conditioned and the unknown deterministic parameter vector to be estimated is subjected to known linear constraints as a natural generalization of the gauss markov blue estimator the mv pure estimator is a solution of the following hierarchical nonconvex constrained optimization problem directly related to the mean square error expression in the first stage optimization under a rank constraint we minimize simultaneously all unitarily invariant norms of an operator applied to the unknown parameter vector in view of suppressing bias of the proposed estimator then in the second stage optimization among all pseudo unbiased reduced rank estimators defined as the solutions of the first stage optimization we find the one achieving minimum variance we derive a closed algebraic form of the mv pure estimator and show that well known estimators the gauss markov blue estimator the generalized marquardt s reduced rank estimator and the minimum variance conditionally unbiased affine estimator subject to linear restrictions are all special cases of the mv pure estimator we demonstrate the effectiveness of the proposed estimator in a numerical example where we employ the mv pure estimator to the ill conditioned problem of reconstructing a 2 d image subjected to linear constraints from blurred noisy observation this example demonstrates that the mv pure estimator outperforms all aforementioned estimators as it achieves smaller mean square error for all values of signal to noise ratio

extreme nonnegative matrices abstract an entrywise nonnegative n n matrix a is extreme if its spectrum 1 n has the property that for all 0 1 n is not the spectrum of a nonnegative matrix it is proved that if a is an extreme nonnegative matrix then there exists a nonzero nonnegative matrix y such that ay ya and at y 0 where is the hadamard or entrywise product and t denotes transpose

fir filter representations of reduced rank noise reduction we show that the reduced rank output signal computed via truncated q svd is identical to that from an array of parallelly connected analysis synthesis finite impulse response fir filter pairs the filter coefficients are determined by the q svd and the filters provide an explicit description of the reduced rank noise reduction algorithm in the frequency domain

stochastic mv pure estimator robust reduced rank estimator for stochastic linear model this paper proposes a novel linear estimator named stochastic mv pure estimator developed for the stochastic linear model and designed to provide improved performance over the linear minimum mean square error mmse wiener estimator in cases prevailing in practical real world settings where at least some of the second order statistics of the random vectors under consideration are only imperfectly known the proposed estimator shares its main mathematical idea and terminology with the recently introduced minimum variance pseudo unbiased reduced rank estimator mv pure developed for the linear regression model the proposed stochastic mv pure estimator minimizes the mean square error mse of its estimates subject to rank constraint and inducing minimum distortion to the target random vector therefore the stochastic mv pure combines the techniques of the reduced rank wiener filter named in this paper rr mmse and the distortionless constrained estimator named in this paper c mmse in order to achieve greater robustness against noise or model errors than rr mmse and c mmse furthermore to ensure that the stochastic mv pure estimator combines the reduced rank and minimum distortion approaches in the mse optimal way we propose a rank selection criterion which minimizes the mse of the estimates obtained by the stochastic mv pure as a numerical example we employ the stochastic mv pure rr mmse c mmse and mmse estimators as linear receivers in a mimo wireless communication system this example is chosen as a typical signal processing scenario where the statistical information on the data on which the estimates are built is only imperfectly known we verify that the stochastic mv pure achieves the lowest mse and symbol error rate ser in such settings by employing the proposed rank selection criterion

construction of nonnegative symmetric matrices with given spectrum abstract let 1 n be the spectrum of a nonnegative symmetric matrix a with the perron eigenvalue 1 a diagonal entry c and let 1 m be the spectrum of a nonnegative symmetric matrix b with the perron eigenvalue 1 we show how to construct a nonnegative symmetric matrix c with the spectrum 1 max 0 1 c 2 n 2 m

applications of a brauer theorem in the nonnegative inverse eigenvalue problem abstract a result by brauer which shows how to modify one single eigenvalue of a matrix without changing any of the remaining eigenvalues plays a relevant role in the study of the nonnegative inverse eigenvalue problem niep perfect in a long time ignored paper 1955 presents an extension of this result which shows how to modify r eigenvalues of a matrix of order n r n via a rank r perturbation without changing any of the n r remaining eigenvalues by using this extension perfect gives a realizability criterion for the real niep which is not contained in soto s realizability criterion in this work by extending perfect s result we give a new realizability criterion for the real niep which contains soto s criterion thus this new realizability criterion appears to be the most general sufficient condition for the real niep so far we also contribute to the solution of the symmetric niep for n 5

guo perturbation for symmetric nonnegative circulant matrices abstract guo w guo eigenvalues of nonnegative matrices linear algebra appl 266 1997 261 270 sets the question if the list 1 2 n is symmetrically realizable that is is the spectrum of a symmetric nonnegative matrix and t 0 whether or not the list t 1 t 2 t 3 n is also symmetrically realizable in this paper we give an affirmative answer to this question in the case that the realizing matrix is circulant or left circulant we also give a necessary and sufficient condition for to be the spectrum of a nonnegative left circulant matrix

an inverse eigenvalue problem for nonnegative matrices abstract this paper gives a solution to an inverse eigenvalue problem of nonnegative matrices which was proposed by miroslav fiedler

analytical numerical investigation of bubble type solutions of nonlinear singular problems in this work we are concerned about a singular boundary value problem for a second order nonlinear ordinary differential equation arising in hydrodynamics and nonlinear field theory when centrally symmetric bubble type solutions are sought we are interested on solutions of this equation which are strictly increasing on the positive semi axis and have finite limits at zero and infinity necessary conditions for the existence of such solutions are obtained in the form of a restriction on the equation parameters the asymptotic behavior of certain solutions of this equation is analyzed near the two singularities when r 0 and r where the considered boundary conditions define one parameter families of solutions based on the analytic study an efficient numerical method is proposed to compute approximately the needed solutions of the above problem some results of the numerical experiments are displayed and their physical interpretation is discussed

a characterization of trace zero bisymmetric nonnegative 5 5 matrices abstract let 1 2 3 4 5 1 be real numbers such that i 1 5 i 0 in 16 o spector proved that a necessary and sufficient condition for 1 2 3 4 5 to be the eigenvalues of a traceless symmetric nonnegative 5 5 matrix is 2 5 0 and i 1 5 i 3 0 in this article we show that this condition is also a necessary and sufficient condition for 1 2 3 4 5 to be the spectrum of a traceless bisymmetric nonnegative 5 5 matrix

an inverse eigenvalue problem for symmetric and normal matrices abstract some new sufficient conditions are found for n real numbers to be the spectrum of some n n symmetric nonnegative matrix and for n complex numbers to be the spectrum of some n n normal nonnegative matrix