In this paper we illustrate that paraorthogonality on the unit circle $\mathbb{T}$ is the counterpart to orthogonality on $\mathbb{R}$ when we are interested in the spectral properties. We characterize quasi-paraorthogonal polynomials on the unit circle as the analogues of the quasi-orthogonal polynomials on $\mathbb{R}$. We analyze the possibilities of preselecting some of its zeros, in order to build positive quadrature formulas with prefixed nodes and maximal domain of validity. These quadrature formulas on the unit circle are illustrated numerically.

翻译：在本文中,我们可以说明单位圆 $\mathbb{T}$ 是当我们对光谱属性感兴趣时对 $\ mathbb{R}$ 的正方位公式的对应方。 我们将单位圆上的准单方位多球形定性为 $\ mathbb{R}$ 的准正方位数。 我们分析了预选一些零的可能性, 以建立正方位方位公式, 以预设节点和最大有效性域。 单位圆上的这些二次方位公式用数字表示 。