An application of matrix calculus to an engineering problem.
An approach based on matrix polynomials for linear systems of partial differential equations
In this paper, an approach based on matrix polynomials is introduced for solving linear systems of partial differential equations. The main feature of the proposed method is the computation of the Smith canonical form of the assigned matrix polynomial to the linear system of PDEs, which leads to a reduced system. It will be shown that the reduced one is an independent system of PDEs having only one unknown in each equation. A comparison of the results for several test problems reveals that the method...
An easily computable invariant of trilinear alternating forms
An efficient algorithm for computing real powers of a matrix and a related matrix function
The paper is devoted to an algorithm for computing matrices and for a given square matrix and a real . The algorithm uses the binary expansion of and has the logarithmic computational complexity with respect to . The problem stems from the control theory.
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