Salatiga’s income as a function of tax and retribution
DETERMINATION PARAMETER BY NONLINEAR LEAST SQUARE
H.A Parhusip
1
1
Department of Industrial Mathematics and Statistics, Faculty of Science and Mathematics ,
Satya Wacana Christian University, Indonesia _________________________________________________________________________
Abstract.
Determination parameter from the given data by nonlinear least square is discussed here. The case study is expressing Salatiga’s income as a function of tax and retribution using calculus multivari-
able. The function is then used in the system of ordinary differential equation. Its equilibrium point is obtained by using trust region algorithm since the equilibrium is the solution of the governing nonlinear
system. The solutions of nonlinear ordinary differential equations are also presented.
Keywords
: nonlinear least square, nonlinear equations, equilibrium points.
1.
Introduction
This research is motivated by a limitation of knowledge in many branches of mathematics for undergraduate. On the other hand, students face various data from the small companies and government
in their surroundings. With some branches in mathematics, students have difficulties to integrate their knowledge to the given data and one has to analyze data with various interests. Therefore this paper pro-
vides the basic idea on this direction.
Frequently, determination of parameters leads to solving nonlinear system such that the chosen function fit to the given data especially in the case of nonlinear system. Motor parameter determination
for transient torque calculations for example, Pragasen, et.all [1997] applied genetic algorithms and com- pared to Newton-Raphson method.
On this paper we present that the function has two variables and its parameters determined by nonlinear least square as shown by Stoer and Bulirsch [1991] whereby we try to minimize the average
square deviation of the approximating function on a set of selected points. Since data are multivariable, one may use multivariate calculus and choose a certain function. We expect the function has special
properties such as an existence of minimizer, boundedness, continuity and differentiability in the given domain of definition. The minimization problem reduces into a problem of solving nonlinear system.
Therefore one has to choose an available algorithm to solve the system. Some algorithms are available in software packages such as MATLAB. However difficulties may appear to make a good initial guess to
use an available algorithm.
Salatiga is one of the small cities in Central Java, Indonesia. There are some sectors provide the income to the Department of Financial in Salatiga Dinas Pengelolaan Keuangan Daerah Salatiga. The
case study is an analysis of the income as a function of city’s tax and retribution given by society. We assume that other sectors are not significant.
This paper is organized as follows. Derivation of Salatiga’s income as a function of tax and ret- ribution and a competition model are presented in Section 2. Procedures to develop the models and theirs
solutions are shown in Section 3. Finally, the Section 4 shows the result and the Conclusion is stated in the Section 5.