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.
Approximations and error bounds for computing the inverse mapping
In this paper we propose a procedure to construct approximations of the inverse of a class of differentiable mappings. First of all we determine in terms of the data a neighbourhood where the inverse mapping is well defined. Then it is proved that the theoretical inverse can be expressed in terms of the solution of a differential equation depending on parameters. Finally, using one-step matrix methods we construct approximate inverse mappings of a prescribed accuracy.
Areas of certain polygons in connection with determinants of rectangular matrices.
Arithmetical graphs.
Aspects of non-commutative function theory
We discuss non commutative functions, which naturally arise when dealing with functions of more than one matrix variable.
Asymptotic analysis of powers of matrices.
Asymptotic Behaviour of Variable-Coefficient Toeplitz Determinants.
Asymptotic enumeration of dense 0-1 matrices with equal row sums and equal column sums.
Asymptotic variance of functionals of discrete-time Markov chains via the Drazin inverse.
Asymptotics for weakly dependent errors-in-variables
Linear relations, containing measurement errors in input and output data, are taken into account in this paper. Parameters of these so-called errors-in-variables (EIV) models can be estimated by minimizing the total least squares (TLS) of the input-output disturbances. Such an estimate is highly non-linear. Moreover in some realistic situations, the errors cannot be considered as independent by nature. Weakly dependent (- and -mixing) disturbances, which are not necessarily stationary nor identically...
Asymptotics of the partition function of a random matrix model
We prove a number of results concerning the large asymptotics of the free energy of a random matrix model with a polynomial potential. Our approach is based on a deformation of potential and on the use of the underlying integrable structures of the matrix model. The main results include the existence of a full asymptotic expansion in even powers of of the recurrence coefficients of the related orthogonal polynomials for a one-cut regular potential and the double scaling asymptotics of the free...
Automorphismen und Antiautomorphismen von Tensoralgebren.
Axioms for invariant factors.