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MOC
1998
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13 years 10 months ago
Numerical solution of parabolic integro-differential equations by the discontinuous Galerkin method
The numerical solution of a parabolic equation with memory is considered. The equation is first discretized in time by means of the discontinuous Galerkin method with piecewise co...
Stig Larsson, Vidar Thomée, Lars B. Wahlbin
MOC
1998
96views more  MOC 1998»
13 years 10 months ago
A convergence theorem for the fast multipole method for 2 dimensional scattering problems
Abstract. The Fast Multipole Method (FMM) designed by V. Rokhlin rapidly computes the field scattered from an obstacle. This computation consists of solving an integral equation o...
Christophe Labreuche
MOC
1998
64views more  MOC 1998»
13 years 10 months ago
Trapezoidal and midpoint splittings for initial-boundary value problems
In this paper we consider various multi-component splittings based on the trapezoidal rule and the implicit midpoint rule. It will be shown that an important requirement on such me...
Willem Hundsdorfer
MOC
1998
65views more  MOC 1998»
13 years 10 months ago
A note on stability of the Douglas splitting method
In this note some stability results are derived for the Douglas splitting method. The relevance of the theoretical results is tested for an advection-reaction equation.
Willem Hundsdorfer
MOC
1998
106views more  MOC 1998»
13 years 10 months ago
Bounds for eigenvalues and condition numbers in the p-version of the finite element method
In this paper, we present a theory for bounding the minimum eigenvalues, maximum eigenvalues, and condition numbers of stiffness matrices arising from the p-version of finite ele...
Ning Hu, Xian-Zhong Guo, I. Norman Katz
MOC
1998
94views more  MOC 1998»
13 years 10 months ago
Numerical calculation of the multiplicity of a solution to algebraic equations
A method to calculate numerically the multiplicity of a solution to a system of algebraic equations is presented. The method is an application of Zeuthen’s rule which gives the m...
Hidetsune Kobayashi, Hideo Suzuki, Yoshihiko Sakai
MOC
1998
65views more  MOC 1998»
13 years 10 months ago
A natural lattice basis problem with applications
Integer lattices have numerous important applications, but some of them may have been overlooked because of the common assumption that a lattice basis is part of the problem instan...
John D. Hobby
MOC
1998
71views more  MOC 1998»
13 years 10 months ago
Factorizing complex symmetric matrices with positive definite real and imaginary parts
Complex symmetric matrices whose real and imaginary parts are positive definite are shown to have a growth factor bounded by 2 for LU factorization. This result adds to the classe...
Nicholas J. Higham
MOC
1998
65views more  MOC 1998»
13 years 10 months ago
A generalized discrepancy and quadrature error bound
An error bound for multidimensional quadrature is derived that includes the Koksma-Hlawka inequality as a special case. This error bound takes the form of a product of two terms. O...
Fred J. Hickernell
MOC
1998
65views more  MOC 1998»
13 years 10 months ago
Solving constrained Pell equations
Consider the system of Diophantine equations x2 − ay2 = b, P (x, y) = z2, where P is a given integer polynomial. Historically, such systems have been analyzed by using Baker’s ...
Kiran S. Kedlaya