Displaying similar documents to “A matrix constructive method for the analytic-numerical solution of coupled partial differential systems”

Analytic enclosure of the fundamental matrix solution

Roberto Castelli, Jean-Philippe Lessard, Jason D. Mireles James (2015)

Applications of Mathematics

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This work describes a method to rigorously compute the real Floquet normal form decomposition of the fundamental matrix solution of a system of linear ODEs having periodic coefficients. The Floquet normal form is validated in the space of analytic functions. The technique combines analytical estimates and rigorous numerical computations and no rigorous integration is needed. An application to the theory of dynamical system is presented, together with a comparison with the results obtained...

Latent roots of lambda-matrices, Kronecker sums and matricial norms

José S. L. Vitória (1980)

Aplikace matematiky

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Kronecker sums and matricial norms are used in order to give a method for determining upper bounds for A where A is a latent root of a lambda-matrix. In particular, upper bounds for z are obtained where z is a zero of a polynomial with complex coefficients. The result is compared with other known bounds for z .

The Re-nonnegative definite solutions to the matrix equation A X B = C

Qing Wen Wang, Chang Lan Yang (1998)

Commentationes Mathematicae Universitatis Carolinae

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An n × n complex matrix A is called Re-nonnegative definite (Re-nnd) if the real part of x * A x is nonnegative for every complex n -vector x . In this paper criteria for a partitioned matrix to be Re-nnd are given. A necessary and sufficient condition for the existence of and an expression for the Re-nnd solutions of the matrix equation A X B = C are presented.

Using successive approximations for improving the convergence of GMRES method

Jan Zítko (1998)

Applications of Mathematics

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In this paper, our attention is concentrated on the GMRES method for the solution of the system ( I - T ) x = b of linear algebraic equations with a nonsymmetric matrix. We perform m pre-iterations y l + 1 = T y l + b before starting GMRES and put y m for the initial approximation in GMRES. We derive an upper estimate for the norm of the error vector in dependence on the m th powers of eigenvalues of the matrix T . Further we study under what eigenvalues lay-out this upper estimate is the best one. The estimate shows and...

A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix

Fuad Kittaneh (2003)

Studia Mathematica

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It is shown that if A is a bounded linear operator on a complex Hilbert space, then w ( A ) ≤ 1 / 2 ( | | A | | + | | A ² | | 1 / 2 ) , where w(A) and ||A|| are the numerical radius and the usual operator norm of A, respectively. An application of this inequality is given to obtain a new estimate for the numerical radius of the Frobenius companion matrix. Bounds for the zeros of polynomials are also given.