Order Stars: Theory and Applications

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CRC Press, Jun 1, 1991 - Science - 248 pages
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According to Hilbert's dictum, the scaffolding should be invisible in a math ematical edifice. Less kind interpretation of this common principle of writing and presenting mathematics is that we should always strive to do it baek to-front, forever wise after the event. Nobody should be allowed to see the seams in the supposedly seamless robe or eompare authors' intentions with the outeome of their endeavour. In particular, the short pieee of prose oeea sionally labelIed 'Prefaee' or 'Forward' ought to be written after the main body of the book. And so it is, and we, the authors, can refleet (with much trepidation) on an enterprise that for us is finally over. Order stars have been originally introduced in the context of numerical solution of ordinary differential equations and, as far as many numerical an alysts are concerned, they still belong there. It is our case in this book that the seope of order stars ranges considerably wider and that the cornerstone of the order star theory is a function-theoretic interpretation of complex approximation theory. An application to numerical analysis is a matter of serendipity, not of essen ce.
  

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Contents

General order stars
9
Rational approximants to the exponential
28
Aacceptability barriers
50
Multistep methods
92
The advection equation
120
The diffusion equation
155
Fade approximants
177
Contractive approximation
193
Open problems
207
Advection equation with two space
224
Name index
239
Copyright

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Page 235 - One-step methods of Hermite type for numerical integration of stiff systems, BIT 14 (1974) 63-77.
Page 235 - Attainable Order of Rational Approximations to the Exponential Function with only real Poles, BIT 17 (1977, 200-208.
Page 231 - Rational approximations to the exponential function with two complex conjugate interpolation points. SIAM J.
Page 228 - Akhiezer, NI (1965), The classical moment problem, Oliver and Boyd, Edinburgh and London. [2] Ashurst, WT and Meiron, D. (1987), "Numerical Study of Vortex Reconnection,

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