1,144 research outputs found
Efficient Rank Reduction of Correlation Matrices
Geometric optimisation algorithms are developed that efficiently find the
nearest low-rank correlation matrix. We show, in numerical tests, that our
methods compare favourably to the existing methods in the literature. The
connection with the Lagrange multiplier method is established, along with an
identification of whether a local minimum is a global minimum. An additional
benefit of the geometric approach is that any weighted norm can be applied. The
problem of finding the nearest low-rank correlation matrix occurs as part of
the calibration of multi-factor interest rate market models to correlation.Comment: First version: 20 pages, 4 figures Second version [changed content]:
21 pages, 6 figure
Computation of saddle type slow manifolds using iterative methods
This paper presents an alternative approach for the computation of trajectory
segments on slow manifolds of saddle type. This approach is based on iterative
methods rather than collocation-type methods. Compared to collocation methods,
that require mesh refinements to ensure uniform convergence with respect to
, appropriate estimates are directly attainable using the method of
this paper. The method is applied to several examples including: A model for a
pair of neurons coupled by reciprocal inhibition with two slow and two fast
variables and to the computation of homoclinic connections in the
FitzHugh-Nagumo system.Comment: To appear in SIAM Journal of Applied Dynamical System
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