Looking for a faster way to analyze large, sparse matrices? This paper introduces a new dynamically shifted power iteration technique, dashSVD, designed to improve the accuracy and efficiency of randomized singular value decomposition (SVD) algorithms. Aimed at computing a few of the largest singular values and vectors, the dashSVD algorithm incorporates techniques for handling sparse matrices and includes an accuracy-control mechanism to monitor vector error bounds. An accuracy-control mechanism approximates and monitors the per vector error bound of computed singular vectors with negligible overhead. The dashSVD algorithm collaborates with the skills for handling sparse matrices. Experiments on real-world data validate that the dashSVD algorithm largely improves the accuracy of randomized SVD algorithm or attains same accuracy with fewer passes over the matrix. Data from real-world tests demonstrate that dashSVD enhances the accuracy of randomized SVD and delivers an efficient accuracy-control mechanism, showcasing its advantages in runtime and parallel efficiency. The paper also provides a bound on the approximation error of randomized SVD with the shifted power iteration, making it useful for computer science and applied mathematics.
Published in ACM Transactions on Mathematical Software, this research fits squarely within the journal's focus on algorithms and software for mathematical problem-solving. The dashSVD algorithm, designed for efficient singular value decomposition, is a direct contribution to the field of mathematical software and computation. Its advantages in accuracy, runtime, and parallel efficiency align with the journal's emphasis on practical and effective software solutions.