An Efficient Method for Calculating Smoothing Splines Using Orthogonal Transformations.
An eigenvalue inequality and spectrum localization for complex matrices.
An eigenvector pattern arising in non linear regression.
Let A = (aij) be an n x n matrix defined by aij = aji = i, i = 1,...,n. This paper gives some elementary properties of A and other related matrices. The eigenstructure of A is conjectured: given an eigenvector v of A the remaining eigenvectors are obtained by permuting up to sign the components of v. This problem arises in a distance based method applied to non linear regression.
An elementary proof of Hadamard's theorem
An envelope for the spectrum of a matrix
We introduce and study an envelope-type region ɛ(A) in the complex plane that contains the eigenvalues of a given n×n complex matrix A. ɛ(A) is the intersection of an infinite number of regions defined by cubic curves. The notion and method of construction of ɛ(A) extend the notion of the numerical range of A, F(A), which is known to be an intersection of an infinite number of half-planes; as a consequence, ɛ(A) is contained in F(A) and represents an improvement in localizing the spectrum of A.
An equivalent matrix pencilfor bivariate polynomial matrices
In this paper, we present a simple algorithm for the reduction of a given bivariate polynomial matrix to a pencil form which is encountered in Fornasini-Marchesini's type of singular systems. It is shown that the resulting matrix pencil is related to the original polynomial matrix by the transformation of zero coprime equivalence. The exact form of both the matrix pencil and the transformation connecting it to the original matrix are established.
An example of the higher transformation of a binary form.
An Example on Strong Equivalence of Positive Integral Matrices.
An explicit factorization of totally positive generalized Vandermonde matrices avoiding Schur functions.
An explicit formula of Hessian determinants of composite functions and its applications
An extended block Arnoldi algorithm for large-scale solutions of the continuous-time algebraic Riccati equation.
An extension of a result of Lewis.
An extension of the perturbation analysis for the Drazin inverse.
An idempotent algorithm for a class of network-disruption games
A game is considered where the communication network of the first player is explicitly modelled. The second player may induce delays in this network, while the first player may counteract such actions. Costs are modelled through expectations over idempotent probability measures. The idempotent probabilities are conditioned by observational data, the arrival of which may have been delayed along the communication network. This induces a game where the state space consists of the network delays. Even...
An identity between the determinant and the permanent of Hessenberg-type matrices
In this short note we provide an extension of the notion of Hessenberg matrix and observe an identity between the determinant and the permanent of such matrices. The celebrated identity due to Gibson involving Hessenberg matrices is consequently generalized.
An implementation of the fast Givens transformations on a MIMD computer
An improved characterisation of the interior of the completely positive cone.
An improvement of an inequality of Fiedler leading to a new conjecture on nonnegative matrices
Suppose that is an nonnegative matrix whose eigenvalues are . Fiedler and others have shown that , for all , with equality for any such if and only if is the simple cycle matrix. Let be the signed sum of the determinants of the principal submatrices of of order , . We use similar techniques to Fiedler to show that Fiedler’s inequality can be strengthened to: , for all . We use this inequality to derive the inequality that: . In the spirit of a celebrated conjecture due to Boyle-Handelman,...
An improvement of Kaplansky's lemma on locally algebraic operators
An inclusion region for the field of values of a doubly stochastic matrix based on its graph.