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- Franz Peherstorfer, Knut Petras
- SIAM J. Numerical Analysis
- 2000

- Knut Petras
- Adv. Comput. Math.
- 2000

- Knut Petras
- Numerical Algorithms
- 2001

For many numerical problems involving smooth multivariate functions on d-cubes, the so-called Smolyak algorithm (or Boolean method, sparse grid method, etc.) has proved to be very useful. The final form of the algorithm (see equation (12) below) requires functional evaluation as well as the computation of coefficients. The latter can be done in different… (More)

- Markus Grimmer, Knut Petras, Nathalie Revol
- Numerical Software with Result Verification
- 2003

We give a survey on packages for multiple precision interval arithmetic, with the main focus on three specific packages. One is within a Maple environment, intpakX, and two are C/C++ libraries, GMP-XSC and MPFI. We discuss their different features, present timing results and show several applications from various fields, where high precision intervals are… (More)

- Knut Petras
- Numerical Algorithms
- 1995

Explicit bounds for the quadrature error of thenth Gauss-Legendre quadrature rule applied to themth Chebyshev polynomial are derived. They are precise up to the orderO(m 4 n −6). As an application, error constants for classes of functions which are analytic in the interior of an ellipse are estimated. The location of the maxima of the corresponding kernel… (More)

- Franz Peherstorfer, Knut Petras
- Numerische Mathematik
- 2003

- Knut Petras
- Numerische Mathematik
- 2003

- Carsten Katscher, Erich Novak, Knut Petras
- J. Complexity
- 1996

We study optimal quadrature formulas for convex functions in several variables. In particular, we answer the following two questions: Are adaptive methods better than nonadaptive ones? And: Are randomized (or Monte Carlo) methods better than deterministic methods?

- Knut Petras
- 1993

- Knut Petras, Klaus Ritter
- J. Complexity
- 2004

We study the intrinsic difficulty of solving linear parabolic initial value problems numerically at a single point. We present a worst case analysis for determin-istic as well as for randomized (or Monte Carlo) algorithms, assuming that the drift coefficients and the potential vary in given function spaces. We use fundamental solutions (parametrix method)… (More)