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：特征向量延拓是一种用于参数化特征值问题的计算方法，它通过在不同参数集下获取的特征向量快照构建基函数，并利用子空间投影技术实现降维求解。该方法属于更广泛的降基方法范畴，是子空间投影技术的重要分支。在本综述文章中，我们系统阐述特征向量延拓及基于投影的仿真器的发展脉络、理论基础与应用实践。首先介绍该方法的核心概念，继而深入探讨其数学原理与收敛特性，最后展示该方法在量子系统领域的最新应用案例并展望其未来发展前景。