interpolating polynomial वाक्य
उदाहरण वाक्य
मोबाइल
- The higher the degree of the interpolating polynomial, the faster the convergence.
- The interpolating polynomial should approximate the given function.
- Calculating the interpolating polynomial is computationally expensive ( see computational complexity ) compared to linear interpolation.
- Choosing the points of intersection as interpolation nodes we obtain the interpolating polynomial coinciding with the best approximation polynomial.
- Additionally, the interpolating polynomial is unique, as shown by the unisolvence theorem at the polynomial interpolation article.
- For more information on formulation of trigonometric interpolating polynomials in the complex plane see, p135 Interpolation using Fourier Polynomials.
- It does not require an interpolating polynomial but instead one has to evaluate the derivative f'in each iteration.
- Neville's algorithm is based on the Newton form of the interpolating polynomial and the recursion relation for the divided differences.
- With the Newton form of the interpolating polynomial a compact and effective algorithm exists for combining the terms to find the coefficients of the polynomial.
- This is indicative of how large degree interpolating polynomial Newton Cotes methods fail to converge for many integrals, while Romberg integration is more stable.
- For every absolutely continuous function on the sequence of interpolating polynomials constructed on Chebyshev nodes converges to " f " ( " x " ) uniformly.
- The disadvantage of Lagrange representation is that any additional point included will increase the order of the interpolating polynomial, leading to the need of recomputing all the fundamental polynomials.
- Does there exist a single table of nodes for which the sequence of interpolating polynomials converge to any continuous function " f " ( " x " )?
- Moreover, the interpolating polynomial is unique if and only if the number of adjustable coefficients is equal to the number of data points, i . e ., " N " = 2 " K " + 1.
- Lyness and Moler showed in 1966 that using undetermined coefficients for the polynomials in Neville's algorithm, one can compute the Maclaurin expansion of the final interpolating polynomial, which yields numerical approximations for the derivatives of the function at the origin.
- There is some subtlety in how one treats the a _ { N } coefficient in the integral, however to avoid double-counting with its alias it is included with weight 1 / 2 in the final approximate integral ( as can also be seen by examining the interpolating polynomial ):
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