8,561 research outputs found
A numerical comparison of discrete Kalman filtering algorithms: An orbit determination case study
The numerical stability and accuracy of various Kalman filter algorithms are thoroughly studied. Numerical results and conclusions are based on a realistic planetary approach orbit determination study. The case study results of this report highlight the numerical instability of the conventional and stabilized Kalman algorithms. Numerical errors associated with these algorithms can be so large as to obscure important mismodeling effects and thus give misleading estimates of filter accuracy. The positive result of this study is that the Bierman-Thornton U-D covariance factorization algorithm is computationally efficient, with CPU costs that differ negligibly from the conventional Kalman costs. In addition, accuracy of the U-D filter using single-precision arithmetic consistently matches the double-precision reference results. Numerical stability of the U-D filter is further demonstrated by its insensitivity of variations in the a priori statistics
Non-negative matrix factorization for self-calibration of photometric redshift scatter in weak lensing surveys
Photo-z error is one of the major sources of systematics degrading the
accuracy of weak lensing cosmological inferences. Zhang et al. (2010) proposed
a self-calibration method combining galaxy-galaxy correlations and galaxy-shear
correlations between different photo-z bins. Fisher matrix analysis shows that
it can determine the rate of photo-z outliers at a level of 0.01-1% merely
using photometric data and do not rely on any prior knowledge. In this paper,
we develop a new algorithm to implement this method by solving a constrained
nonlinear optimization problem arising in the self-calibration process. Based
on the techniques of fixed-point iteration and non-negative matrix
factorization, the proposed algorithm can efficiently and robustly reconstruct
the scattering probabilities between the true-z and photo-z bins. The algorithm
has been tested extensively by applying it to mock data from simulated stage IV
weak lensing projects. We find that the algorithm provides a successful
recovery of the scatter rates at the level of 0.01-1%, and the true mean
redshifts of photo-z bins at the level of 0.001, which may satisfy the
requirements in future lensing surveys.Comment: 12 pages, 6 figures. Accepted for publication in ApJ. Updated to
match the published versio
Implication of the Branching Ratios for the CKM Phenomenology
We study the implication of the recent measurement by the BELLE collaboration
of the averaged branching fraction for the CKM phenomenology.
Combined with the averaged branching fraction measured earlier, this yields for the ratio of the two
branching fractions. Updating earlier theoretical analysis of these decays
based on the QCD factorization framework, and constraining the CKM-Wolfenstein
parameters from the unitarity fits, our results yield and , in agreement with the
BELLE data. Leaving instead the CKM-Wolfenstein parameters free, our analysis
gives (at 68% C.L.) , which is in agreement
with but less precise than the indirect CKM-unitarity fit of the same, . The isospin-violating ratio in the decays and the SU(3)-violating ratio in the decays are presented together with estimates of the direct and
mixing-induced CP-asymmetries in the decays within
the SM. Their measurements will overconstrain the angle of the
CKM-unitarity triangle.Comment: 21 pages, 3 figures. Included a discussion of model-dependent
estimates of the long-distance/rescattering contributions in radiative
B-decays; added a reference. Version accepted for publication in Physics
Letters
Relaxed Majorization-Minimization for Non-smooth and Non-convex Optimization
We propose a new majorization-minimization (MM) method for non-smooth and
non-convex programs, which is general enough to include the existing MM
methods. Besides the local majorization condition, we only require that the
difference between the directional derivatives of the objective function and
its surrogate function vanishes when the number of iterations approaches
infinity, which is a very weak condition. So our method can use a surrogate
function that directly approximates the non-smooth objective function. In
comparison, all the existing MM methods construct the surrogate function by
approximating the smooth component of the objective function. We apply our
relaxed MM methods to the robust matrix factorization (RMF) problem with
different regularizations, where our locally majorant algorithm shows
advantages over the state-of-the-art approaches for RMF. This is the first
algorithm for RMF ensuring, without extra assumptions, that any limit point of
the iterates is a stationary point.Comment: AAAI1
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