A method for the inverse numerical range problem.
A Method of Solving the Stability Problem for Complex Matrices.
A Minimaximin Formula and its Application to Doubly Stochastic Matrices
A modified Cayley transform for the discretized Navier-Stokes equations
This paper is concerned with the problem of computing a small number of eigenvalues of large sparse generalized eigenvalue problems. The matrices arise from mixed finite element discretizations of time dependent equations modelling viscous incompressible flow. The eigenvalues of importance are those with smallest real part and are used to determine the linearized stability of steady states, and could be used in a scheme to detect Hopf bifurcations. We introduce a modified Cayley transform of the...
A multiplication theorem for two-variable positive real matrices
A multiplication-division theorem is derived for the positive real functions of two complex variables. The theorem is generalized to encompass the product of positive real functions of two complex variables. The theorem is generalized to encompass the product of positive real matrices whose elements are functions of two complex variables. PRF and PR matrices occur frequantly in the study of electrical multiports and multivariable systems (such as digital filters).
A multishift algorithm for the numerical solution of algebraic Riccati equations.
A necessary and sufficient condition for stability of the convex combination of polynomials
A necessary and sufficient condition for the existence of a unique solution of a discrete boundary value problem.
A necessary and sufficient eigenvector condition for a connected graph to be bipartite.
A nested multiplicative commutator equation
A new characterization of generalized complementary basic matrices
In this paper, a new characterization of previously studied generalized complementary basic matrices is obtained. It is in terms of ranks and structure ranks of submatrices defined by certain diagonal positions. The results concern both the irreducible and general cases.
A New Characterization of Generalized Complementary Basic Matrices
In this paper, a new characterization of previously studied generalized complementary basic matrices is obtained. It is in terms of ranks and structure ranks of submatrices defined by certain diagonal positions. The results concern both the irreducible and general cases
A new decomposition for square matrices.
A new determinant expression of the zeta function for a hypergraph.
A new equivalent condition of the reverse order law for -inverses of multiple matrix products.
A new family of companion forms of polynomial matrices.
A new family of spectrally arbitrary ray patterns
An ray pattern is called a spectrally arbitrary ray pattern if the complex matrices in give rise to all possible complex polynomials of degree . In a paper of Mei, Gao, Shao, and Wang (2014) was proved that the minimum number of nonzeros in an irreducible spectrally arbitrary ray pattern is . In this paper, we introduce a new family of spectrally arbitrary ray patterns of order with exactly nonzeros.
A new Geršgorin-type eigenvalue inclusion set.
A new inclusion interval for the real eigenvalues of real matrices
By properties of Cvetković-Kostić-Varga-type (or, for short, CKV-type) B-matrices, a new class of nonsingular matrices called CKV-type -matrices is given, and a new inclusion interval of the real eigenvalues of real matrices is presented. It is shown that the new inclusion interval is sharper than those provided by J. M. Peña (2003), and by H. B. Li et al. (2007). We also propose a direct algorithm for computing the new inclusion interval. Numerical examples are included to illustrate the effectiveness...
A new proof of a theorem about generalized orthogonal polynomials.