论文标题
一类平面代数曲线的正交多项式
Orthogonal polynomials on a class of planar algebraic curves
论文作者
论文摘要
我们构建双变量正交多项式（ops），上的代数曲线，$ y^m = ϕ（x）$ in $ \ mathbb {r}^2 $中，$ m = 1、2 $和$ d $是任意度的多项式$ d $，在单位分析中，在单位上是单变量的$ d $。我们计算将双变量OPS与本身是正交且跨度包含OP作为子空间的多项式基础的连接系数。连接矩阵显示为带子，并且通过$ o（nd^4）$操作的lanczos算法计算了$ 0，\ ldots，n $的连接系数和jacobi矩阵。
We construct bivariate orthogonal polynomials (OPs) on algebraic curves of the form $y^m = ϕ(x)$ in $\mathbb{R}^2$ where $m = 1, 2$ and $ϕ$ is a polynomial of arbitrary degree $d$, in terms of univariate semiclassical OPs. We compute connection coeffeicients that relate the bivariate OPs to a polynomial basis that is itself orthogonal and whose span contains the OPs as a subspace. The connection matrix is shown to be banded and the connection coefficients and Jacobi matrices for OPs of degree $0, \ldots, N$ are computed via the Lanczos algorithm in $O(Nd^4)$ operations.
