For minimization problems without 2nd derivative information, methods that
estimate Hessian ma- trices can be very effective. However, conventional
techniques generate dense matrices that are prohibitive for large problems.
Limited-memory compact representations express the dense arrays in terms of a
low rank representation and have become the state-of-the-art for software
implementations on large deterministic problems. We develop new compact
representations that are parameterized by a choice of vectors and that reduce
to existing well known formulas for special choices. We demonstrate
effectiveness of the compact representations for large eigenvalue computations,
tensor factorizations and nonlinear regressions.

无需二阶导数信息的最小化问题，通过估计 Hessian 矩阵的方法可以非常有效。然而，传统技术产生的密集矩阵对于大型问题来说是不可行的。有限内存紧凑表示以低秩表示方式表达密集数组，并成为大型确定性问题软件实现的最新技术。我们开发了一种新的紧凑表示方法，通过选择向量进行参数化，并对特定选择的现有公式进行减少。我们展示了紧凑表示在大量特征值计算、张量分解和非线性回归中的有效性。