Eigenvector continuation is a computational method for parametric eigenvalue problems that uses subspace projection with a basis derived from eigenvector snapshots from different parameter sets. It is part of a broader class of subspace-projection techniques called reduced-basis methods. In this colloquium article, we present the development, theory, and applications of eigenvector continuation and projection-based emulators. We introduce the basic concepts, discuss the underlying theory and convergence properties, and present recent applications for quantum systems and future prospects.

翻译：特征向量延续是一种用于参数化特征值问题的计算方法，该方法利用子空间投影，其基函数源自不同参数集下的特征向量快照。它属于更广泛的子空间投影技术类别，即缩减基方法。在本文中，我们介绍了特征向量延续和基于投影仿真器的发展历程、理论基础及实际应用。我们阐述了基本概念，讨论了其背后的理论与收敛性质，并展示了近期在量子系统中的应用成果及未来展望。