I have a quadratic form $\mathbf{x}^T A \mathbf{x}$ (where $A\in \mathbb{R}^{n\times n}$ is symmetric matrix and $\mathbf{x}\in \mathbb{R}^n$) that I want to minimize given the normalization constraint $\mathbf{x}^T\mathbf{x}=1$.Because $\mathbf{A}$ is a adjacency matrix of an undirected graph then I know that it is symmetric and real and also sparse.What is an appropriate memory conservative algorithm to solve this kind of problem?Is it good to solve the eigensystem $\mathbf{A}\mathbf{x}=\lambda \mathbf{x}$ and then taking as solution the first smallest nonzero eigenvalue and its related eigenvector?If this is the way to proceed how is it possible to get the smallest eigenvalue with subspace iteration?
An eigenvalue algorithm to solve constrained quadratic form minimization
optimization;eigensystem