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    • 60. 发明申请
    • Applied estimation of eigenvectors and eigenvalues
    • 特征向量和特征值的应用估计
    • US20050021577A1
    • 2005-01-27
    • US10855174
    • 2004-05-27
    • Nagabhushana PrabhuWei He
    • Nagabhushana PrabhuWei He
    • G06F20060101G06F7/00G06F17/16G06K9/62
    • G06F17/16G06K9/6232
    • Various applications are presented of a vector field method of computing one or more eigenvalues and eigenvectors of a symmetric matrix. The vector field method computes an eigenvector by computing a discrete approximation to the integral curve of a special tangent vector field on the unit sphere. The optimization problems embedded in each iteration of the vector field algorithms admit closed-form solutions making the vector field approach relatively efficient. Among the several vector fields discussed is a family of vector fields called the recursive vector fields. Numerical results are presented that suggest that in some embodiments the recursive vector field method yields implementations that are faster than those based on the QR method. Further, the vector field method preserves, and hence can fully exploit the sparseness on the given matrix to speed up computation even further. Preprocessing that contracts the spectral radius of the given matrix further accelerates the systems.
    • 呈现了用于计算对称矩阵的一个或多个特征值和特征向量的矢量场方法的各种应用。 矢量场方法通过计算单位球上特殊切线矢量场的积分曲线的离散近似来计算特征向量。 嵌入在矢量场算法的每次迭代中的优化问题承认封闭形式的解决方案,使得矢量场方法相对有效。 在讨论的几个矢量场中,有一系列称为递归矢量场的矢量场。 提出了数值结果,表明在一些实施例中,递归矢量场方法产生比基于QR方法的实现更快的实现。 此外,矢量场方法保留,因此可以充分利用给定矩阵上的稀疏度,进一步加速计算。 收缩给定矩阵的光谱半径的预处理进一步加速了系统。