An Introduction to Programming with Mathematica®

Wellin, Paul R.; Gaylord, Richard J.; Kamin, Sam

doi:10.1017/cbo9780511801303

Cited by 34 publications

(15 citation statements)

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“…Nevertheless, we have verified that these operations can be performed with well-known symbolic analysis software, such as Mathematica [7]. The resulting expressions are composed of simple logarithmic and inverse of trigonometric functions, depending only on the size cell dimensions.…”

Section: A Identities and Integrals For Rectangular Domainsmentioning

confidence: 88%

Analytical Evaluation of the Static MoM Terms for Volume and Surface Rectangular Domains

Soler

Pereira

Álvarez‐Melcón

et al. 2010

Antennas Wirel. Propag. Lett.

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Abstract-We present a simple analytical implementation of the static singular integrals arising in the volume/surface integral equation formulation for the analysis of mixed conducting and dielectric structures such as printed circuits with finite-size dielectric objects. The singularity of the Green's functions is extracted from the kernel of the integral equation as a static term. This term is then evaluated analytically for coincident rectangular cells in two and three dimensions. The new technique allows an accurate and efficient evaluation of method of moments (MoM) self-interactions compared to other methods previously used in the literature.

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Section: A Identities and Integrals For Rectangular Domainsmentioning

confidence: 88%

Analytical Evaluation of the Static MoM Terms for Volume and Surface Rectangular Domains

Soler

Pereira

Álvarez‐Melcón

et al. 2010

Antennas Wirel. Propag. Lett.

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“…Para os valores de perturbações menores testados, não podemos distinguir estatisticamente os dois espectros. Para mais informações sobre programação em Mathematica, veja [9].…”

Section: Considerações Finaisunclassified

Comparação Estatística de Autovalores de um Operador de Schrödinger Perturbado

Artuso

Marim

2020

Rev. Bras. Ensino Fís.

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Recebido em 23 de setembro de 2019. Revisado em 18 de janeiro de 2020. Aceito em 25 de janeiro de 2020 Nesse trabalho introduzimos os operadores de Schrödinger de forma ingênua e despretensiosa, mas munida de certa precisão e didática. São mencionados os tipos de potenciais mais estudados, os periódicos e os aleatórios e, via simulação numérica, comparados os autovalores da matriz truncada de um operador munido de um potencial periódico e com este mesmo potencial perturbado por uma variável aleatória contínua com distribuição uniforme. Avaliamos qual a magnitude necessária da variável aleatória para produzir diferença significativa entre os conjuntos de autovalores. Palavras-chave: Operadores de Schrödinger, potencial periódico, potencial perturbado.In this paper we introduce Schrödinger's operators in a naive and unpretentious way, but with some precision and didactics. The most studied periodic and random potential types are mentioned and, by numerical simulation, compare the eigenvalues of an operator's truncated matrix with a periodic potential and the same potential disturbed by an evenly distributed continuous random variable. We evaluated the magnitude of the random variable required to produce a significant difference between the eigenvalue sets.

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“…If the iterates produced via the iteration scheme converges a zero of the polynomial applying the condition |g(x k )| ≤ 10 −2 and a maximum of 100 iterates, we decide that z 0 is in the attraction basin of the zero and we specify this node by some color. 18,19 Accordingly, this behavior is plotted in Figure 1 (left), while its density plot for large domains are given in It is remarked that the global convergence behavior of the main contributed method (14) can be investigated theoretically in a similar way to equations (17) to (21) of Soleymani et al 20, pages 4-5 Several discussions regarding the derivation, application, and convergence behavior of nonlinear equation solvers for tackling matrix problems specially of nonlinear type such as sign function, square root of a matrix, and polar decomposition have been reported in some literatures such as in Khaksar Haghani and Soleymani 16 and the references therein. Now, it is straightforward to naïvely extend (14) to matrix environment and uniquely attain…”

Section: Derivation Of a Novel Iterative Schemementioning

confidence: 99%

A fast iterative method to find the matrix geometric mean of two HPD matrices

Jebreen

Akgül

2019

Math Methods in App Sciences

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The purpose of this research is to present a novel scheme based on a quick iterative scheme for calculating the matrix geometric mean of two Hermitian positive definite (HPD) matrices. To do this, an iterative scheme with global convergence is constructed for the sign function using a novel three‐step root‐solver. It is proved that the new scheme is convergent and shown to have global convergence behavior for this target, when square matrices having no pure imaginary eigenvalues. Next, the constructed scheme is used and extended through a well‐known identity for the calculation of the matrix geometric mean of two HPD matrices. Ultimately, several experiments are collected to show its usefulness.

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An Introduction to Programming with Mathematica®

Cited by 34 publications

References 0 publications

Analytical Evaluation of the Static MoM Terms for Volume and Surface Rectangular Domains

Analytical Evaluation of the Static MoM Terms for Volume and Surface Rectangular Domains

Comparação Estatística de Autovalores de um Operador de Schrödinger Perturbado

A fast iterative method to find the matrix geometric mean of two HPD matrices

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