2,497 research outputs found
Faster Geometric Algorithms via Dynamic Determinant Computation
The computation of determinants or their signs is the core procedure in many
important geometric algorithms, such as convex hull, volume and point location.
As the dimension of the computation space grows, a higher percentage of the
total computation time is consumed by these computations. In this paper we
study the sequences of determinants that appear in geometric algorithms. The
computation of a single determinant is accelerated by using the information
from the previous computations in that sequence.
We propose two dynamic determinant algorithms with quadratic arithmetic
complexity when employed in convex hull and volume computations, and with
linear arithmetic complexity when used in point location problems. We implement
the proposed algorithms and perform an extensive experimental analysis. On one
hand, our analysis serves as a performance study of state-of-the-art
determinant algorithms and implementations. On the other hand, we demonstrate
the supremacy of our methods over state-of-the-art implementations of
determinant and geometric algorithms. Our experimental results include a 20 and
78 times speed-up in volume and point location computations in dimension 6 and
11 respectively.Comment: 29 pages, 8 figures, 3 table
Sub-matrix updates for the Continuous-Time Auxiliary Field algorithm
We present a sub-matrix update algorithm for the continuous-time auxiliary
field method that allows the simulation of large lattice and impurity problems.
The algorithm takes optimal advantage of modern CPU architectures by
consistently using matrix instead of vector operations, resulting in a speedup
of a factor of and thereby allowing access to larger systems and
lower temperature. We illustrate the power of our algorithm at the example of a
cluster dynamical mean field simulation of the N\'{e}el transition in the
three-dimensional Hubbard model, where we show momentum dependent self-energies
for clusters with up to 100 sites
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