Why does the polyfit() function in Matlab use Vandermonde-matrix and QR factorization method to solve a system of equations?

7 次查看（过去 30 天）
Poorna
Poorna 2012-11-9
The polyfit() function in Matlab can be used for least-squares curve fit for any given polynomial order. The method used by Matlab is to construct the Vandermonde matrix and then solve it via QR factorization.
However, why doesn't Matlab use a more direct method for solving a system of linear equations using the conditions for least-squares fit and matrix-inversion methods such as Gauss-eliminaton?

请先登录，再回答此问题。

采纳的回答

Jan
Jan 2012-11-9
The Gauss-elimiation works also, but the QR factorization is more stable here. I do not think that the method you sugeest is "more direct".
  3 个评论
显示 1更早的评论
Jan
Jan 2012-11-10
编辑：Jan 2012-11-10
"Numerically stable" means that small variations of the input do not cause large changes of the output caused by rounding errors. See http://en.wikipedia.org/wiki/Numerical_stability.
Standard examples for a numerically instable method is creating the inverse of A to solve the linear system A*x=b or the simple sum:
sum([1, 1e17, -1e17]) % replies 0
sum([1e17, -1e17, 1]) % replies 1
This means, that the the sum critically depends on the order of input elements.

请先登录，再进行评论。

更多回答（0 个）

类别

在 Help Center 和 File Exchange 中查找有关 Polynomials 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by