We give an explicit solution formula for the polynomial regression problem in terms of Schur polynomials and Vandermonde determinants. We thereby generalize the work of Chang, Deng, and Floater to the case of model functions of the form $\sum _{i=1}^{n} a_{i} x^{d_{i}}$ for some integer exponents $d_{1} >d_{2} >\dotsc >d_{n} \geq 0$ and phrase the results using Schur polynomials. Even though the solution circumvents the well-known problems with the forward stability of the normal equation, it is only of practical value if $n$ is small because the number of terms in the formula grows rapidly with the number $m$ of data points. The formula can be evaluated essentially without rounding.

翻译：我们给出了以舒尔多项式和范德蒙德行列式表达的多项式回归问题的显式解公式。由此将Chang、Deng和Floater的工作推广至模型函数形式为$\sum _{i=1}^{n} a_{i} x^{d_{i}}$（其中整数指数$d_{1} >d_{2} >\dotsc >d_{n} \geq 0$）的情形，并利用舒尔多项式表述结果。尽管该解法规避了正规方程前向稳定性中众所周知的问题，但由于公式中的项数随数据点数量$m$快速增长，仅当$n$较小时才具有实际应用价值。该公式在评估时基本不产生舍入误差。