Displaying similar documents to “A General Numerical Approach to Sensitivity Analysis and Error Analysis with Adjoint Systems”

Loss of Accuracy in Numerical Computations Загуба на точност в числените пресмятания

Konstantinov, Mihail, Petkov, Petko (2011)

Union of Bulgarian Mathematicians

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Михаил М. Константинов, Петко Х. Петков - Разгледани са възможните катастрофални ефекти от неправилното използване на крайна машинна аритметика с плаваща точка. За съжаление, тази тема не винаги се разбира достатъчно добре от студентите по приложна и изчислителна математика, като положението в инженерните и икономическите специалности в никакъв случай не е по-добро. За преодоляване на този образователен пропуск тук сме разгледали главните виновници за загубата на точност при числените компютърни...

Computing the numerical range of Krein space operators

Natalia Bebiano, J. da Providência, A. Nata, J.P. da Providência (2015)

Open Mathematics

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Consider the Hilbert space (H,〈• , •〉) equipped with the indefinite inner product[u,v]=v*J u,u,v∈ H, where J is an indefinite self-adjoint involution acting on H. The Krein space numerical range WJ(T) of an operator T acting on H is the set of all the values attained by the quadratic form [Tu,u], with u ∈H satisfying [u,u]=± 1. We develop, implement and test an alternative algorithm to compute WJ(T) in the finite dimensional case, constructing 2 by 2 matrix compressions of T and their...

A comparison of the accuracy of the finite-difference solution to boundary value problems for the Helmholtz equation obtained by direct and iterative methods

Václav Červ, Karel Segeth (1982)

Aplikace matematiky

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The development of iterative methods for solving linear algebraic equations has brought the question of when the employment of these methods is more advantageous than the use of the direct ones. In the paper, a comparison of the direct and iterative methods is attempted. The methods are applied to solving a certain class of boundary-value problems for elliptic partial differential equations which are used for the numerical modeling of electromagnetic fields in geophysics. The numerical...