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MOC
2011
13 years 7 days ago
Fast evaluation of modular functions using Newton iterations and the AGM
We present an asymptotically fast algorithm for the numerical evaluation of modular functions such as the elliptic modular function j. Our algorithm makes use of the natural connec...
Régis Dupont
MOC
2011
12 years 11 months ago
Class numbers of ray class fields of imaginary quadratic fields
Let K be an imaginary quadratic field with class number one and let p ⊂ OK be a degree one prime ideal of norm p not dividing 6dK . In this paper we generalize an algorithm of S...
Omer Kucuksakalli
MOC
2011
13 years 7 days ago
Local energy estimates for the finite element method on sharply varying grids
Abstract. Local energy error estimates for the finite element method for elliptic problems were originally proved in 1974 by Nitsche and Schatz. These estimates show that the loca...
Alan Demlow, Johnny Guzmán, Alfred H. Schat...
MOC
2011
13 years 7 days ago
Exponential convergence and tractability of multivariate integration for Korobov spaces
In this paper we study multivariate integration for a weighted Korobov space for which the Fourier coefficients of the functions decay exponentially fast. This implies that the fu...
Josef Dick, Gerhard Larcher, Friedrich Pillichsham...
MOC
2011
12 years 8 months ago
Calculating cyclotomic polynomials
Abstract. We present three algorithms to calculate Φn(z), the nth cyclotomic polynomial. The first algorithm calculates Φn(z) by a series of polynomial divisions, which we perfo...
Andrew Arnold, Michael B. Monagan