Accurate computation of eigenvalues for prolate spheroidal wave functions

Sinha, B.P.; MacPhie, R.H.; Prasad, T. Rajendra

doi:10.1109/tap.1973.1140487

Cited by 18 publications

(6 citation statements)

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“…The radius of convergence, R, is particularly investigated by studying the properties of the power series, and some of them are revealed. The current power series is computed with a double precision accuracy for |c| < R and is verified via numerical algorithms [1,[13][14][15]. The coefficients of the power series are related to each other by a recursion relation that facilitates the calculation of higher-order coefficients.…”

Section: Introductionmentioning

confidence: 99%

Accurate power series for eigenvalues of spheroidal angle functions and their convergence radii

Do-NhatTam¹

2011

Can. J. Phys.

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In this paper, the radius of convergence of the spheroidal power series associated with the eigenvalue is calculated without using the branch point approach. Studying the properties of the power series using the recursion relations among its coefficients in the new method offers some insights into the spheroidal power series and its associated eigenfunction. This study also used the least squares method to accurately compute the convergence radii to five or six significant digits. Within the circle of convergence in the complex plane of the parameter c = kF, where k is the wavenumber and F is the semifocal length of the spheroidal system, the extremely fast convergent spheroidal power series are computed with full precision. In addition, a formula for the magnitude of the upper bound of the error is obtained.Résumé : Nous calculons ici le rayon de convergence de la série de puissance sphéroïdale associée aux valeurs propres sans utiliser l'approche du point de branchement. L'étude des propriétés des séries de puissance par méthode récursive entre les coefficients est une approche qui offre une nouvelle perception des séries de puissance sphéroïdales et des fonctions propres associées. Nous utilisons la méthode des moindres carrés pour calculer de façon précise les rayons de convergence à cinq ou six chiffres significatifs. Les séries de puissance à convergence extrêmement rapide sont calculées avec une complète précision à l'intérieur du rayon de convergence dans le plan complexe du paramètre c = kF, où k est le nombre d'onde et F la demi-longueur focale du système sphéroïdal. Nous obtenons aussi une formule donnant la limite d'erreur supérieure du calcul.[Traduit par la Rédaction]

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Section: Introductionmentioning

confidence: 99%

Accurate power series for eigenvalues of spheroidal angle functions and their convergence radii

Do-NhatTam¹

2011

Can. J. Phys.

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“…1. Many researchers have obtained the electromagnetic field vectors inside and outside the oblate spheroids with various methods, such as analytical and infinite element methods [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. In the present study, we obtained the calculation results in the oblate coordinate system (g, n, /) using the analytical method used by Asano [5,12].…”

Section: Scattering Field Vectorsmentioning

confidence: 99%

Optical characteristics of flowing blood

et al. 2011

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The transmitted light strength (TS) through a thin blood layer changes with variation in blood flow, such as positive streaming transparency for low hematocrits and negative streaming transparency for high hematocrits. These phenomena are examined theoretically and experimentally. Maxwell's equations are solved assuming that erythrocytes are oblate spheroids to investigate these phenomena due to flowing blood. The theoretical results reveal that the scattering and absorption cross sections for flowing blood are larger than those for stagnant blood. Experimental results indicate that the TS for both oxygenated and deoxygenated flowing blood, with a hematocrit of up to approximately 20%, was stronger than that for stagnant blood. The TS decreased for flowing blood with a hematocrit of approximately 20% or greater. Applying the theoretical scattering and absorption cross sections to the absorption and multiple scattering theory of Victor Twersky, the changes in the TS due to flowing blood are obtained theoretically. From the theoretical and experimental results, the positive streaming transparency phenomenon of flowing blood with a low hematocrit and the negative streaming transparency phenomenon with a high hematocrit are found to result from increased scattering and absorption cross sections because of the orientation of flowing erythrocytes.

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“…Meixner [2] 1.1274 Flammer [4] 1.12773 A&S [5] 1.127734 segv [9] 1.127734064849934 SMP [19] 1.127734064849931 swf-8…”

Section: Softwarementioning

confidence: 99%

“…Here N = 100 was used throughout for simplicity. Results from [2, p. 323], [4, p. 97] and the 11 values in [19] are included. Table 1 shows typical results.…”

Section: Eigenvaluesmentioning

confidence: 99%

Calculation of spheroidal wave functions

Kirby¹

2006

Computer Physics Communications

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Accurate computation of eigenvalues for prolate spheroidal wave functions

Cited by 18 publications

References 1 publication

Accurate power series for eigenvalues of spheroidal angle functions and their convergence radii

Accurate power series for eigenvalues of spheroidal angle functions and their convergence radii

Optical characteristics of flowing blood

Calculation of spheroidal wave functions

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