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MOC
1998
65views more  MOC 1998»
13 years 9 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
MOC
1998
71views more  MOC 1998»
13 years 9 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
96views more  MOC 1998»
13 years 9 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
66views more  MOC 1998»
13 years 9 months ago
Nonconforming finite element approximation of crystalline microstructure
Abstract. We consider a class of nonconforming finite element approximations of a simply laminated microstructure which minimizes the nonconvex variational problem for the deforma...
Bo Li, Mitchell Luskin
MOC
1998
102views more  MOC 1998»
13 years 9 months ago
Classification of integral lattices with large class number
A detailed exposition of Kneser’s neighbour method for quadratic lattices over totally real number fields, and of the sub-procedures needed for its implementation, is given. Usi...
Rudolf Scharlau, Boris Hemkemeier