First Course in Numerical Methods

Jennings, Walter

doi:10.2307/2003624

Cited by 14 publications

(2 citation statements)

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“…Additionally, the standard numerical integration methods (e.g. approximation by a sum of areas) are notoriously unstable [49][50][51], making non-linear least-squares fitting problematic.…”

Section: Analysis: Beyond the Product Function Approximationmentioning

confidence: 99%

“…With the full analytic form of f z (s) (equation ( 21)) a more accurate, stable and faster numerical calculation of G z (t) is possible as w(z) converges to the required accuracy with a simple four-to six-term geometric series. This avoids the necessity of integrating f z (s) in equation (20), which in terms of calculation time is much more costly as well as much less numerically stable [49][50][51] than the above method.…”

Section: Dynamic Lineshape Calculationsmentioning

confidence: 99%

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Zero-field muon spin relaxation studies of frustrated magnets: physics and analysis issues

Ryan¹,

Lierop²,

Cadogan³

2004

J. Phys.: Condens. Matter

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The exquisite sensitivity of zero-field muon spin relaxation to both static magnetic order and dynamic fluctuations has been used to study the ordering processes in a variety of exchange frustrated magnetic materials. Two distinct ordering events are identified, and they each clearly show both dynamic and static signatures. Phase diagrams for two classes of frustration are presented. We also provide an extensive discussion of both approximate and complete solutions to dynamic fitting functions, and show that the correct functions used in our analysis yield more accurate fits and quantitative agreement with independent measurements on the same samples.

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“…Additionally, the standard numerical integration methods (e.g. approximation by a sum of areas) are notoriously unstable [49][50][51], making non-linear least-squares fitting problematic.…”

Section: Analysis: Beyond the Product Function Approximationmentioning

confidence: 99%