![]() Which can be written as follows in matrix form: To find the unique polynomial of degree that passes through data points, we need to solve a linear set of equations with the coefficients of the polynomial being the unknowns. So, if two degree polynomials and agree on points, then, their difference is a polynomial of degree but has roots which implies that. This fact relies on the Fundamental Theorem of Algebra that states that every degree polynomial has exactly roots. Polynomial interpolation relies on the fact that for every data points, there is a unique polynomial of degree that passes through these data points. The polynomial equation for each curve is shown in the title for each graph. Figure 1 shows fitting polynomials of degrees 1, 2, 3, and 4, to sets of 2, 3, 4, and 5 data points. If we have three data points, then we can fit a polynomial of the second degree (a parabola) that passes through the three points. For example, if we have two data points, then we can fit a polynomial of degree 1 (i.e., a linear function) between the two points. Polynomial interpolation is the procedure of fitting a polynomial of degree to a set of data points. Polynomial Interpolation Introduction to Polynomial Interpolation Open Educational Resources Introduction to Numerical Analysis: ![]()
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