The Implicit QL Algorithm

Dubrulle, Augustin A.; Martin, R. S.; Wilkinson, J. H.

doi:10.1007/978-3-662-39778-7_15

Cited by 3 publications

(4 citation statements)

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“…The increased computing cost will be substantially reduced if the solution is based on a diagonalization process analogous to that described in section 4.5.2. If special boundary conditions prevent the use of a fast diagonalization algorithm, it will still be economical to compute once the eigensystem of the pertinent difference operator in x by conventional methods (Schwarz 1971, Martin, Reinsch, and Wilkinson 1971, Dubrulle, Martin, and Wilkinson 1971 for repeated usage. The same comment applies to the method based on the mixed approximation.…”

Section: Resultsmentioning

confidence: 99%

On Numerical Methods for Migration in Layered Media*

Dubrulle¹

1983

Geophysical Prospecting

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Three current migration methods derived from the wave‐equation model and based on approximations by Fourier series, finite‐differences, and a combination of both (mixed method) are reviewed. Each method is examined in the context of horizontally layered media, where the velocity of wave propagation varies with depth alone. It is shown how, under such conditions, the special properties of the linear equations obtained from finite‐difference and mixed approximations can be exploited for computational efficiency. A numerical algorithm is described which substantially reduces the complexity and the computational cost of the solution. This algorithm is directly applicable to vector processing. The description of each method includes derivation, dispersion relation, stability properties, and applicable numerical algorithms. Comparative analyses show that, for the same computational cost, the finite‐difference approximation has poor accuracy characteristics and should be used only when the boundary conditions are difficult to express in the frequency domain. The results are illustrated with numerical experiments on synthetic data.

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Section: Resultsmentioning

confidence: 99%

On Numerical Methods for Migration in Layered Media*

Dubrulle¹

1983

Geophysical Prospecting

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“…The algorithm becomes very simple and has been shown to be very efficient when it is applied to a real symmetric tridiagonal matrix (Bowdler et al, 1971). However, when the elements of the tridiagonal matrix differ widely in order of magnitude, severe loss of accuracy may be experienced in the computation of the eigenvalues of smaller magnitude (Dubrulle et al, 1971).…”

Section: Computational Strategiesmentioning

confidence: 99%

“…This loss of accuracy can be avoided to some extent by employing the implicit QL algorithm of Dubrulle et al (1971).…”

Section: Computational Strategiesmentioning

confidence: 99%