Fast algorithms for floating-point interval matrix multiplication
Fast algorithms for floating-point interval matrix multiplication
复制标题
浮点区间矩阵乘法的快速算法
DOI：
10.1016/j.cam.2011.10.011
复制
发表时间：
2012
期刊：
影响因子：
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通讯作者：
S. Oishi
中科院分区：
文献类型：
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作者：
K. Ozaki;T. Ogita;S. Rump;S. Oishi
讨论了真实的区间矩阵乘法的几种方法。首先介绍了区间矩阵乘法快速算法的早期研究：朴素区间算法、Oishi-Rump的中点半径形式的区间算法及其快速变体Ogita-Oishi。接下来，开发了三种新的快速算法。所提出的算法需要一个，两个或三个矩阵的产品，分别。关键在于，我们的算法可以快速预测哪些项将成为区间计算中的主导半径。我们提出了一种混合方法来预测哪种算法适合优化性能和结果的宽度。数值算例表明了算法的有效性。
We discuss several methods for real interval matrix multiplication. First, earlier studies of fast algorithms for interval matrix multiplication are introduced: naive interval arithmetic, interval arithmetic by midpoint–radius form by Oishi–Rump and its fast variant by Ogita–Oishi. Next, three new and fast algorithms are developed. The proposed algorithms require one, two or three matrix products, respectively. The point is that our algorithms quickly predict which terms become dominant radii in interval computations. We propose a hybrid method to predict which algorithm is suitable for optimizing performance and width of the result. Numerical examples are presented to show the efficiency of the proposed algorithms.
影响因子：
2.7
作者：
Goto, Kazushige;Van De Geijn, Robert
通讯作者：
Van De Geijn, Robert
影响因子：
2.1
作者：
通讯作者：
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