Difference between revisions of "Main Page"
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<math display="block">\begin{matrix} |
<math display="block">\begin{matrix} |
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| − | \text{Using |
+ | \text{Using Polynomials as a Form-Fitting Tool.} \\ |
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\\ |
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| − | \text{By |
+ | \text{By Dirk Mittler, August 16, 2013} \\ |
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\\ |
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| − | \text{As |
+ | \text{As an example, a cubic (3rd-order) polynomial can be given as follows:} \\ |
\\ |
\\ |
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{f{{(x)}=\mathit{a1}}{x^{3} + \mathit{a2}}{x^{2} + \mathit{a3}}{x + \mathit{a4}}.} \\ |
{f{{(x)}=\mathit{a1}}{x^{3} + \mathit{a2}}{x^{2} + \mathit{a3}}{x + \mathit{a4}}.} \\ |
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\\ |
\\ |
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| − | \text{This |
+ | \text{This type of function can be made to give a list of 4 values, for a list of 4 known} \\ |
| − | \text{parameters |
+ | \text{parameters (x), through a careful choice of a1 ... a4 :} \\ |
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\\ |
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{\mathit{a1}{x_{1}^{3} + \mathit{a2}}{x_{1}^{2} + \mathit{a3}}{{x_{1} + \mathit{a4}}=f}{(x_{1})}.} \\ |
{\mathit{a1}{x_{1}^{3} + \mathit{a2}}{x_{1}^{2} + \mathit{a3}}{{x_{1} + \mathit{a4}}=f}{(x_{1})}.} \\ |
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[math]\displaystyle{ y=\sqrt{1-x^{2}} }[/math]
[math]\displaystyle{ \begin{matrix} \text{Using Polynomials as a Form-Fitting Tool.} \\ \\ \text{By Dirk Mittler, August 16, 2013} \\ \\ \text{As an example, a cubic (3rd-order) polynomial can be given as follows:} \\ \\ {f{{(x)}=\mathit{a1}}{x^{3} + \mathit{a2}}{x^{2} + \mathit{a3}}{x + \mathit{a4}}.} \\ \\ \text{This type of function can be made to give a list of 4 values, for a list of 4 known} \\ \text{parameters (x), through a careful choice of a1 ... a4 :} \\ \\ {\mathit{a1}{x_{1}^{3} + \mathit{a2}}{x_{1}^{2} + \mathit{a3}}{{x_{1} + \mathit{a4}}=f}{(x_{1})}.} \\ {\mathit{a1}{x_{2}^{3} + \mathit{a2}}{x_{2}^{2} + \mathit{a3}}{{x_{2} + \mathit{a4}}=f}{(x_{2})}.} \\ {\mathit{a1}{x_{3}^{3} + \mathit{a2}}{x_{3}^{2} + \mathit{a3}}{{x_{3} + \mathit{a4}}=f}{(x_{3})}.} \\ {\mathit{a1}{x_{4}^{3} + \mathit{a2}}{x_{4}^{2} + \mathit{a3}}{{x_{4} + \mathit{a4}}=f}{(x_{4})}.} \\ \\ \end{matrix} }[/math]
