WeChat Mini Program
Old Version Features

    • Three Double Multi-Step Randomized Extended Kaczmarz Methods for Solving Large Sparse Inconsistent Linear Systems

    Zhi-Min Xu,Hai-Long Shen,Xin-Hui Shao

    Comput Appl Math（2025）

    Northeastern University

    Cited 0|Views9
    Abstract
    In order to solve large sparse inconsistent linear equations more efficiently and accurately, based on the multi-step randomized extended Kaczmarz method, we propose three double multi-step randomized extended Kaczmarz algorithms. Firstly, we introduce the double multi-step randomized extended Kaczmarz (DMREK) algorithm with probability criteria, where the selection of parameters is based on the order of coefficient matrix, and the convergence of this algorithm has been proven. Additionally, we propose two new algorithms, namely the double randomized multi-step randomized extended Kaczmarz (DRMREK) algorithm with random parameters and the residual-based randomized multi-step randomized extended Kaczmarz (RRMREK) algorithm. Numerical experimental results demonstrate that the three new algorithms DMREK, DRMREK, and RRMREK perform well. And the RRMREK algorithm, along with others, demonstrates advantages in terms of the number of iteration steps.
    More
    Translated text
    Key words
    Kaczmarz algorithm,Randomized extended Kaczmarz algorithm,Double multi-step randomized extended Kaczmarz,Inconsistent linear systems,65F08,65F10,65FXX
    求助PDF
    上传PDF
    View via Publisher
    Bibtex
    AI Read Science
    AI Summary
    AI Summary is the key point extracted automatically understanding the full text of the paper, including the background, methods, results, conclusions, icons and other key content, so that you can get the outline of the paper at a glance.
    Example
    Background
    Key content
    Introduction
    Methods
    Results
    Related work
    Fund
    Key content
    • Pretraining has recently greatly promoted the development of natural language processing (NLP)
    • We show that M6 outperforms the baselines in multimodal downstream tasks, and the large M6 with 10 parameters can reach a better performance
    • We propose a method called M6 that is able to process information of multiple modalities and perform both single-modal and cross-modal understanding and generation
    • The model is scaled to large model with 10 billion parameters with sophisticated deployment, and the 10 -parameter M6-large is the largest pretrained model in Chinese
    • Experimental results show that our proposed M6 outperforms the baseline in a number of downstream tasks concerning both single modality and multiple modalities We will continue the pretraining of extremely large models by increasing data to explore the limit of its performance
    Upload PDF to Generate Summary
    Must-Reading Tree
    Example
    Generate MRT to find the research sequence of this paper
    Data Disclaimer
    The page data are from open Internet sources, cooperative publishers and automatic analysis results through AI technology. We do not make any commitments and guarantees for the validity, accuracy, correctness, reliability, completeness and timeliness of the page data. If you have any questions, please contact us by email: report@aminer.cn
    Chat Paper
    Summary is being generated by the instructions you defined