| 摘要: |
| 矩阵求逆运算作为信号处理的基础运算在数字信号处理、无线通信技术等领域中得到广泛应用。然而在处理较高条件数的矩阵求逆运算时，浮点计算舍入误差的累积效应会被显著放大，传统的矩阵求逆方法难以获得可信的数值结果。为解决该问题，利用无误差变换技术，在工作精度（双精度）下，实现了双倍双精度浮点运算，并基于数字信号处理器开发了双倍双精度基本运算函数库。在此基础上，设计并实现了基于QR分解的双倍双精度矩阵求逆技术。通过大量不同类型矩阵的数值实验，表明所提算法显著降低了矩阵求逆计算的误差，对条件数较大的矩阵仍能实现可靠的矩阵求逆计算。 |
| 关键词: 矩阵求逆 无误差变换 双倍双精度算法 舍入误差 |
| DOI：10.20079/j.issn.1001-893x.240930002 |
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| 基金项目:四川省自然科学基金创新研究群体项目（2024NSFTD0053）；四川省自然科学基金（2023NSFSC0497） |
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| Double-Double Precision Matrix Inverse Technique Based on DSP |
| XIN Zhenni,CHEN Ying,XI Guojiang |
| (1.Southwest China Institute of Electronic Technology，Chengdu 610036，China;2.Agile and Intelligent Computing Key Laboratory of Sichuan Province，Chengdu 610036，China) |
| Abstract: |
| The matrix inverse operation is widely utilized as a fundamental procedure in signal processing within the domains of digital signal processing and wireless communication technology.However，when encountering matrix inverse computations with poorly conditioned matrices，the amplification of round-off errors in floating-point calculations poses a significant challenge in obtaining accurate numerical results using conventional matrix inverse methods.To address this issue，error-free transformation technology is used to achieve double-double precision floating-point operations within the working precision(double precision).Additionally，a double-double precision basic operation function library is developed on the digital signal processor，upon which a double-double precision matrix inverse technique based on QR decomposition is formulated and implemented.By conducting numerous numerical experiments on matrices of varying characteristics，it has been proved that the proposed algorithm greatly diminishes the error in matrix inversion calculations and effectively accomplishes reliable matrix inversion for matrices with high-condition numbers. |
| Key words: matrix inverse error-free transformation double-double-precision algorithm round-off error |
《电讯技术》编辑部 