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.

翻译：对于缺乏二阶导数信息的优化问题，估计Hessian矩阵的方法通常非常有效。然而，传统技术会生成稠密矩阵，这在处理大规模问题时难以实现。有限内存紧凑表示通过低秩表示来表达稠密数组，已成为解决大规模确定性问题的软件实现中的先进技术。我们开发了由向量选择参数化的新紧凑表示，并在特定选择下简化为现有已知公式。我们展示了紧凑表示在大规模特征值计算、张量分解和非线性回归中的有效性。