# Approximate Analytical Solutions for the Weight Optimization Problems of CI and ICI

2017-10-12
Approximate analytical formulae are proposed for the solutions of the weight optimization problems involved in Covariance Intersection (CI) and Inverse Covariance Intersection (ICI). The methodology used for obtaining the analytic approximations boils down to using just two Newton iterations with the initial weight value 1/2. The simulation results show that quite acceptable root-mean-square (RMS) error levels are achievable with the proposed approximate analytical weights with less computations compared to what would be required when numerical optimization with a high termination tolerance is used, which can be critical for applications with very limited computational resources.

# Suggestions

 Exact solutions of the Schrodinger equation via Laplace transform approach: pseudoharmonic potential and Mie-type potentials Arda, Altug; Sever, Ramazan (Springer Science and Business Media LLC, 2012-04-01) Exact bound state solutions and corresponding normalized eigenfunctions of the radial Schrodinger equation are studied for the pseudoharmonic and Mie-type potentials by using the Laplace transform approach. The analytical results are obtained and seen that they are the same with the ones obtained before. The energy eigenvalues of the inverse square plus square potential and three-dimensional harmonic oscillator are given as special cases. It is shown the variation of the first six normalized wave-functions ...
 Exact Solutions of Some Partial Differential Equations Using the Modified Differential Transform Method Cansu Kurt, Ümmügülsüm; Ozkan, Ozan (2018-03-01) In this paper, we present the modification of the differential transform method by using Laplace transform and Pade approximation to obtain closed form solutions of linear and nonlinear partial differential equations. Some illustrative examples are given to demonstrate the activeness of the proposed technique. The obtained results ensure that this modified method is capable of solving a large number of linear and nonlinear PDEs that have wide application in science and engineering. It solves the drawbacks i...
 Differential constrains, recursion operators, and logical integrability Satir, A (Springer Science and Business Media LLC, 1997-10-01) Differential constraints compatible with the linearized equations of partial differential equations are examined. Recursion operators are obtained by integrating the differential constraints.
 Bound-state solutions of the Klein-Gordon equation for the generalized PT-symmetric Hulthen potential Egrifes, Harun; Sever, Ramazan (2007-04-01) The one-dimensional Klein-Gordon equation is solved for the PT-symmetric generalized Hulthen potential in the scalar coupling scheme. The relativistic bound-state energy spectrum and the corresponding wave functions are obtained by using the Nikiforov-Uvarov method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type.
 Evaluation of Hypersingular Integrals on Non-planar Surfaces Selcuk, Gokhun; Koç, Seyit Sencer (2014-05-16) Solving electric field integral equation (EFIE) with Nystrom method requires accurate evaluation of hypersingular surface integrals since this method does not use divergence conforming basis and testing functions. The success of the method also depends on accurate representation of non-planar characteristics of the scattering object. In this study Hadamard finite part interpretation is used to evaluate hypersingular integrals over non-planar surfaces, which are represented by their Taylor series expansions....
Citation Formats
U. Orguner, “Approximate Analytical Solutions for the Weight Optimization Problems of CI and ICI,” 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/53658. 