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Contents

D. N. Arnold, A. Mukherjee &L. Pouly: Adaptive finite elements and
colliding black holes 1

C. J. Budd &G. J. Collins: Symmetry based numerical methods for
partial differential equations 16

R. H. Byrd, Guanghui Liu &J. Nocedal: On the local behavior of an
interior point method for nonlinear programming 37

A. J. Cox &N. J. Higham: Stability of Householder QR factorization for
weighted least squares problems 57

J. E. Flaherty, R. M. Loy, M. Dindar, M. S. Shephard, B. K. Szymanski,
J. D. Teresco &L. H. Ziantz: An adaptive and parallel framework for
partial differential equations 74

R. Fletcher: Block triangular orderings and factors for sparse matrices in LP 91

B. Garc´a-Archilla, J. M. Sanz-Serna &R. D. Skeel: Long-time step methods for
oscillatory differential equations 111

A. Greenbaum: On the role of the left starting vector in the two-sided
Lanczos algorithm and nonsymmetric linear system solvers 124

E. Hairer &P. Leone: Order barriers for symplectic multi-value methods 133

G. F. Jónsson &Ll. N. Trefethen: A numerical analyst looks at the ``cutoff
phenomenon'' in card shuffling and other Markov chains 150

D. Kröner: Finite volume schemes in multidimensions 179

M. J. D. Powell: Trust region calculations revisited 193

G. Strang: The search for a good basis 212

A. J. Wathen, B. Fischer &D. J. Silvester: The convergence of iterative
solution methods for symmetric and indefinite linear systems 230

List of Contributed Talks244