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Remarks on balanced norm error estimates for systems of reaction-diffusion equations

Hans-Goerg Roos (2018)

Applications of Mathematics

Error estimates of finite element methods for reaction-diffusion problems are often realized in the related energy norm. In the singularly perturbed case, however, this norm is not adequate. A different scaling of the H 1 seminorm leads to a balanced norm which reflects the layer behavior correctly. We discuss the difficulties which arise for systems of reaction-diffusion problems.

Remarks on inverse of matrix polynomials

Fischer, Cyril, Náprstek, Jiří (2017)

Programs and Algorithms of Numerical Mathematics

Analysis of a non-classically damped engineering structure, which is subjected to an external excitation, leads to the solution of a system of second order ordinary differential equations. Although there exists a large variety of powerful numerical methods to accomplish this task, in some cases it is convenient to formulate the explicit inversion of the respective quadratic fundamental system. The presented contribution uses and extends concepts in matrix polynomial theory and proposes an implementation...

Remarks on polynomial methods for solving systems of linear algebraic equations

Krzysztof Moszyński (1992)

Applications of Mathematics

For a large system of linear algebraic equations A x = b , the approximate solution x k is computed as the k -th order Fourier development of the function 1 / z , related to orthogonal polynomials in L 2 ( Ω ) space. The domain Ω in the complex plane is assumed to be known. This domain contains the spectrum σ ( A ) of the matrix A . Two algorithms for x k are discussed. Two possibilities of preconditioning by an application of the so called Richardson iteration process with a constant relaxation coefficient are proposed. The case...

Remarks on the economic criterion - the Internal rate of return

Simerská, Carmen (2008)

Programs and Algorithms of Numerical Mathematics

The internal rate of return (IRR) together with the present value (PV) is used as a popular measure for financial project. When used appropriately, it can be a valuable aid in project acceptance or selection. The purpose of this article is to survey the facts about this criterion published so far. More, we investigate the cases of multiple or nonexistent IRRs and try to choose the relevant one and explain its economic meaning.

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