Earticle

To obtain precise information about characteristics of gamma ray detector system responses, we developed new GUIcomputer program to analize full-energy absorption peak using our developed Delphi computer code for educational purpose. By use ofthe well known 4 nonlinear peak shaping functions, peaks were fitted with least square fit method in this code. In this paper, wedescribed the methods to search for 12 coefficients in above 4 nonlinear peak shaping functions by use of our developed code in details.The computer code was tested for 1 µCi 137Cs 661 keV gamma ray peak spectrum detected by 25 % relative efficiency HPGe detectorwith 5.35 cm (D)5.5 cm (L) size.

We study the MATLAB built-in function lsqcurvefit, which solves nonlinear leastsquares curve fitting problems. We describe the optimization problem that the function solves and explain the mechanism of its default solver, the trust-region-reflective method, including the construction of the trust-region subproblem, the reflective handling of bound constraints, and the two-dimensional subspace in which the step is computed. As an illustration of how the function is used in practice, we apply it to the reconstruction of a time-dependent volatility function from option prices governed by the Black-Scholes equation, which we discretize by an implicit finite difference method. Using two sets of manufactured data with known volatility, we recover the volatility by fitting model prices to reference prices with lsqcurvefit and we report the reconstruction errors. The recovered volatilities and the associated option prices agree with the exact ones to high accuracy, which shows that the function reproduces the known answer in this reconstruction, where each interval is fitted as a scalar small-residual problem, and confirms that it is a reliable tool for nonlinear least-squares fitting of this kind. We also apply the same procedure to real market call option prices on the KOSPI200 index, for which a true volatility is not available and the prices carry market noise, and we find that the fitted volatility reproduces the observed prices to within a small root-mean-square error.