Scaled Fixed Point Algorithm for Computing the Matrix Square Root

计算实斜哈密顿矩阵平方根的保结构Schur方法

Structure-preserving Schur methods for computing square roots of real skew-Hamiltonian matrices

针对实斜哈密顿矩阵，提出一种利用其结构特性的Schur方法计算平方根，相比标准实Schur方法大幅减少运算量。

Fast Compensated Algorithms for the Reciprocal Square Root, the Reciprocal Hypotenuse, and Givens Rotations

The reciprocal square root is an important computation for which many very sophisticated algorithms exist (see for example \cite{863046,863031} and the references therein). In this paper we develop a simple differential compensation (much like those developed in \cite{borges}) that can be used to improve the accuracy of a naive calculation. The approach relies on the use of the fused multiply-add (FMA) which is widely available in hardware on a variety of modern computer architectures. We then demonstrate how to combine this approach with a somewhat inaccurate but fast square root free method …

平方根矩阵泛函的泰勒展开

A Taylor expansion of the square root matrix functional

本文提出了一种计算矩阵平方根各阶弗雷歇导数的方法，并给出了高阶泰勒展开式及其积分余项，首次为该类矩阵泛函提供了此类结果。

Zolotarev迭代用于矩阵平方根

Zolotarev Iterations for the Matrix Square Root

本文提出利用Zolotarev有理函数构造矩阵平方根迭代方法，通过递推关系生成高阶最优近似，并在不同极限情况下还原已知迭代形式，适用于特征值幅值差异大的矩阵。

A new stable and avoiding inversion iteration for computing matrix square root

The objective of this research was to compute the principal matrix square root with sparse approximation. A new stable iterative scheme avoiding fully matrix inversion (SIAI) is provided. The analysis on the sparsity and error of the matrices involved during the iterative process is given. Based on the bandwidth and error analysis, a more efficient algorithm combining the SIAI with the filtering technique is proposed. The high computational efficiency and accuracy of the proposed method are demonstrated by computing the principal square roots of different matrices to reveal its applicability o…

A Gaussian method for the operator square root

We consider the approximation of the inverse square root of regularly accretive operators in Hilbert spaces. The approximation is of rational type and comes from the use of the Gauss-Legendre rule applied to a special integral formulation of the problem. We derive sharp error estimates, based on the use of the numerical range, and provide some numerical experiments. For practical purposes, the finite dimensional case is also considered. In this setting, the convergence is shown to be of exponential type.

对"一种用于嵌入式系统能量高效最小二乘计算的无平方根矩阵分解方法"的评论

Comments on "A Square-Root-Free Matrix Decomposition Method for Energy-Efficient Least Square Computation on Embedded Systems"

本文指出，尽管无平方根分解方法在无约束最小二乘问题中有效，但约束问题如MIMO检测仍需计算正交基的范数以获得正确结果。

关于用指数函数进行均方逼近的问题

On root mean square approximation by exponential functions

研究了用有限线性组合的指数函数对平方可积函数进行均方逼近问题，解决线性部分并探讨非线性情况的特定例子。