Client Account:   Login
Home Site Statistics   Contact   About Us   Sunday, March 26, 2017

users on-line: 2 | Forum entries: 6   
j0185201- Back to Home
   Skip Navigation LinksHOME › AREAS OF EXPERTISE › Curve Fitting Solutions › ~ Polynomial Fit Method

"Curve Fitting Solutions"
Polynomial Fit Method

x-array = { , , , , , }
y-array = { , , , , , }

[ Initial x-array: { 0, 1, 2, 3, 4, 5 } ]
[ Initial y-array: { 2, 1, 4, 4, 3, 2 } ]

Polynomial Fit Method

As we mentioned before, please refer to ("Straight Line Fit Method") the polynomial fit is a special case of the linear least squares methods.

Algorithm Creation

In this case, the basis function becomes:

fj(x) = xj,    j = 0,1,...,m

where the matrix and vector in the normal equation become,

Αjk = ∑ni=0  xjj + k,     βk = ∑ni=0  xik yi

Testing the Polynomial Fit Method

In order to test the Polynomial Fit Method as defined above, a new TestPolynomialFit() static method has been added and executed. Supporting code and methods are not shown.

           static void TestPolynomialFit();
                 double[] xarray = new double[] { t1, t2, t3, t4, t5, t6 };
                 double[] yarray = new double[] { t7, t8, t9, t10, t11, t12 };
                    double sigma = 0.0;
                    VectorR results = CurveFitting.PolynomialFit(xarray, yarray, m, out sigma);
                    ListBox1.Items.Add("\nOrder of polynomial m = " + m.ToString() + ",
                       Standard deviation = " + sigma.ToString());
                    ListBox1.Items.Add("Coefficients = " + results.ToString());
                    ListBox1.Items.Add(" ");

As a sample we provide the input data points using two double arrays x-array and y-array. We used the same input function as in ("Straight Line Fit Method"). Running this example generates results shown above. Note the order of the polynomial is given by simple iteration from 1 to 3.

From these results we see that the quadratic polynomial with m = 2:

f(x) = 1.2857 + 1.6x - 0.2857x2

produces the smallest deviation, which can be considered as the best fit to the data.

The user can manipulate all values and try variations on the arrays themselves by specifying new estimate values.

Other Implementations...

Object-Oriented Implementation
Graphics and Animation
Sample Applications
Ore Extraction Optimization
Vectors and Matrices
Complex Numbers and Functions
Ordinary Differential Equations - Euler Method
Ordinary Differential Equations 2nd-Order Runge-Kutta
Ordinary Differential Equations 4th-Order Runge-Kutta
Higher Order Differential Equations
Nonlinear Systems
Numerical Integration
Numerical Differentiation
Function Evaluation

Skip Navigation Links.

Home Skip Navigation Links
   Algorithms, Graphics, Vectors,
            implementation techniques.
   Mineral Transactions info,
            sales, agreements...
   Numerical Modeling services
            mineral environment.
   Want to know about Mining?
            basic knowledge here...
   What are Mineral Commodities?
            our elementary charts.
   Math, Analysis and More...
            our expertise in the matter.


Platform Implementation

Home Algorithm Implementation
We design applications for different environments and platforms...
        Home Graphics and Animation
The graphics classes in Smalltalk were designed...
        Home Optimization Algorithms
An optimization problem is a numerical problem...
        Home Vectors and Matrices
The concise notation introduced in linear algebra for vector...

2017 © Keystone Mining Post  |   2461 E. Orangethorpe Av., Fullerton, CA 92631 USA  |