Antiprojectors with applications in the spectral theory
Application de la généralisation du principe de correspondance à la théorie de l'élimination
Application du théorème de Sylvester à la localisation des valeurs propres de dans le cas symétrique
Application of matrix polynomials to investigation of singular equations.
Application of the Drazin inverse to the analysis of descriptor fractional discrete–time linear systems with regular pencils
Application of the Drazin inverse to the analysis of descriptor fractional discrete-time linear systems with regular pencils
The Drazin inverse of matrices is applied to find the solutions of the state equations of descriptor fractional discrete-time systems with regular pencils. An equality defining the set of admissible initial conditions for given inputs is derived. The proposed method is illustrated by a numerical example.
Application of the partitioning method to specific Toeplitz matrices
We propose an adaptation of the partitioning method for determination of the Moore-Penrose inverse of a matrix augmented by a block-column matrix. A simplified implementation of the partitioning method on specific Toeplitz matrices is obtained. The idea for observing this type of Toeplitz matrices lies in the fact that they appear in the linear motion blur models in which blurring matrices (representing the convolution kernels) are known in advance. The advantage of the introduced method is a significant...
Applications Lineaires Affines Multivoques
Applications of max algebra to diagonal scaling of matrices.
Applications of the characteristic identity for GL(N)
Applications of the Moore-Penrose inverse in digital image restoration.
Applied mathematics meets signal processing.
Approximate polynomial GCD
The computation of polynomial greatest common divisor (GCD) ranks among basic algebraic problems with many applications, for example, in image processing and control theory. The problem of the GCD computing of two exact polynomials is well defined and can be solved symbolically, for example, by the oldest and commonly used Euclid’s algorithm. However, this is an ill-posed problem, particularly when some unknown noise is applied to the polynomial coefficients. Hence, new methods for the GCD computation...
Approximating real linear operators
A framework to extend the singular value decomposition of a matrix to a real linear operator is suggested. To this end real linear operators called operets are introduced, to have an appropriate generalization of rank-one matrices. Then, adopting the interpretation of the singular value decomposition of a matrix as providing its nearest small rank approximations, ℳ is approximated with a sum of operets.
Approximating the isoperimetric number of strongly regular graphs.
Approximation and asymptotics of eigenvalues of unbounded self-adjoint Jacobi matrices acting in l 2 by the use of finite submatrices
We consider the problem of approximation of eigenvalues of a self-adjoint operator J defined by a Jacobi matrix in the Hilbert space l 2(ℕ) by eigenvalues of principal finite submatrices of an infinite Jacobi matrix that defines this operator. We assume the operator J is bounded from below with compact resolvent. In our research we estimate the asymptotics (with n → ∞) of the joint error of approximation for the eigenvalues, numbered from 1 to N; of J by the eigenvalues of the finite submatrix J...
Approximation d’une matrice non inversible par une matrice inversible et -inverse
Approximation of eigenvalues for unbounded Jacobi matrices using finite submatrices
We consider an infinite Jacobi matrix with off-diagonal entries dominated by the diagonal entries going to infinity. The corresponding self-adjoint operator J has discrete spectrum and our purpose is to present results on the approximation of eigenvalues of J by eigenvalues of its finite submatrices.
Approximation of fractional positive stable continuous-time linear systems by fractional positive stable discrete-time systems
Fractional positive asymptotically stable continuous-time linear systems are approximated by fractional positive asymptotically stable discrete-time systems using a linear Padé-type approximation. It is shown that the approximation preserves the positivity and asymptotic stability of the systems. An optional system approximation is also discussed.
Approximation of the minimal Geršgorin set of a square complex matrix.