求解 Bernstein-Vandermonde 线性系统的快速精确算法

Structured inversion of the Bernstein-Vandermonde Matrix

Bernstein polynomials, long a staple of approximation theory and computational geometry, have also increasingly become of interest in finite element methods. Many fundamental problems in interpolation and approximation give rise to interesting linear algebra questions. When attempting to find a polynomial approximation of boundary or initial data, one encounters the Bernstein-Vandermonde matrix, which is found to be highly ill-conditioned. Previously, we used the relationship between monomial Bezout matrices and the inverse of Hankel matrices to obtain a decomposition of the inverse of the Ber…

Bernstein-Vandermonde 矩阵的精确数值线性代数

Accurate numerical linear algebra with Bernstein-Vandermonde matrices

本文利用 Neville 消元法计算全正 Bernstein-Vandermonde 矩阵的双对角分解，从而精确求解线性系统、特征值、奇异值和最小二乘问题。

计算任意维数下拉格朗日插值多项式的贝塞尔控制点

Computing the Bézier Control Points of the Lagrangian Interpolant in Arbitrary Dimension

本文提出了一种计算贝塞尔-瓦尔德蒙矩阵逆的算法，具有与Marco-Martinez算法相同的时间复杂度，并且在多变量情况下有自然推广。