AN ADAPTED CHOLESKY DECOMPOSITION METHOD FOR THE SOLUTION OF COUPLED MAGNETIC‐ELECTRIC EQUATIONS

1989 ◽  
Vol 8 (4) ◽  
pp. 203-208 ◽  
Author(s):  
W. LONG ◽  
F. PIRIOU ◽  
A. RAZEK
Keyword(s):  
Decomposition Method ◽  
Cholesky Decomposition ◽  
Cholesky Decomposition Method

Uncertainty Assessment of Input Parameters for Economic Evaluation: Gauss’s Error Propagation, an Alternative to Established Methods

2009 ◽  
Vol 30 (3) ◽  
pp. 304-313 ◽  
Author(s):  
Björn Stollenwerk ◽  
Stephanie Stock ◽  
Uwe Siebert ◽  
Karl W. Lauterbach ◽  
Rolf Holle
Keyword(s):  
Economic Evaluation ◽  
Standard Deviation ◽  
Parameter Uncertainty ◽  
Error Propagation ◽  
Decomposition Method ◽  
Claims Data ◽  
Cholesky Decomposition ◽  
Uncertainty Assessment ◽  
Propagation Law ◽  
Cholesky Decomposition Method

In decision modeling for health economic evaluation, bootstrapping and the Cholesky decomposition method are frequently used to assess parameter uncertainty and to support probabilistic sensitivity analysis. An alternative, Gauss’s error propagation law, is rarely known but may be useful in some settings. Bootstrapping, the Cholesky decomposition method, and the error propagation law were compared regarding standard deviation estimates of a hypothetic parameter, which was derived from a regression model fitted to simulated data. Furthermore, to demonstrate its value, the error propagation law was applied to German administrative claims data. All 3 methods yielded almost identical estimates of the standard deviation of the target parameter. The error propagation law was much faster than the other 2 alternatives. Furthermore, it succeeded the claims data example, a case in which the established methods failed. In conclusion, the error propagation law is a useful extension of parameter uncertainty assessment.

A decomposition method in non-linear programmm

Optimization ◽  
1975 ◽  
Vol 6 (4) ◽  
pp. 549-559
Author(s):  
L. Gerencsér
Keyword(s):  
Decomposition Method ◽  
Non Linear

DECOMPOSITION METHOD FOR DETERMINING THE HIGH REFLECTED SECTIONS OF A COMPLEX OBJECT SURFACE

2018 ◽  
Vol 77 (11) ◽  
pp. 945-956 ◽  
Author(s):  
N. N. Kolchigin ◽  
M. N. Legenkiy ◽  
A. A. Maslovskiy ◽  
А. Demchenko ◽  
S. Vinnichenko ◽  
...  
Keyword(s):  
Decomposition Method ◽  
Complex Object ◽  
Object Surface

A Spectrum-Adaptive Decomposition Method for Effective Atomic Number Estimation Using Dual Energy CT

2020 ◽  
Vol 2020 (14) ◽  
pp. 293-1-293-7
Author(s):  
Ankit Manerikar ◽  
Fangda Li ◽  
Avinash C. Kak
Keyword(s):  
Atomic Number ◽  
Decomposition Method ◽  
Traditional Approach ◽  
Effective Atomic Number ◽  
Dual Energy ◽  
Performance Comparison ◽  
Estimation Methods ◽  
Dual Energy Ct ◽  
Projection Data ◽  
X Ray

Dual Energy Computed Tomography (DECT) is expected to become a significant tool for voxel-based detection of hazardous materials in airport baggage screening. The traditional approach to DECT imaging involves collecting the projection data using two different X-ray spectra and then decomposing the data thus collected into line integrals of two independent characterizations of the material properties. Typically, one of these characterizations involves the effective atomic number (Zeff) of the materials. However, with the X-ray spectral energies typically used for DECT imaging, the current best-practice approaches for dualenergy decomposition yield Zeff values whose accuracy range is limited to only a subset of the periodic-table elements, more specifically to (Z < 30). Although this estimation can be improved by using a system-independent ρe — Ze (SIRZ) space, the SIRZ transformation does not efficiently model the polychromatic nature of the X-ray spectra typically used in physical CT scanners. In this paper, we present a new decomposition method, AdaSIRZ, that corrects this shortcoming by adapting the SIRZ decomposition to the entire spectrum of an X-ray source. The method reformulates the X-ray attenuation equations as direct functions of (ρe, Ze) and solves for the coefficients using bounded nonlinear least-squares optimization. Performance comparison of AdaSIRZ with other Zeff estimation methods on different sets of real DECT images shows that AdaSIRZ provides a higher output accuracy for Zeff image reconstructions for a wider range of object materials.

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