Shift-Invert Arnoldi Approximation to the Toeplitz Matrix Exponential
Shift-Invert Arnoldi Approximation to the Toeplitz Matrix Exponential
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DOI：
10.1137/090758064
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发表时间：
2010-03
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影响因子：
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通讯作者：
Spike T. Lee;Hong-Kui Pang;Hai-wei Sun
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文献类型：
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作者：
Spike T. Lee;Hong-Kui Pang;Hai-wei Sun
利用移位-逆Arnoldi方法从真实的Toeplitz矩阵和初始向量对应的Krylov子空间生成正交基。利用该方法产生的向量和递推系数对Toeplitz矩阵进行指数逼近。利用Toeplitz矩阵求逆公式和快速Toeplitz矩阵-向量乘法来降低计算量。对于收敛性分析，给出了误差界与矩阵范数无关的充分条件。数值结果证明了该方法的有效性。
The shift-invert Arnoldi method is employed to generate an orthonormal basis from the Krylov subspace corresponding to a real Toeplitz matrix and an initial vector. The vectors and recurrence coefficients produced by this method are exploited to approximate the Toeplitz matrix exponential. Toeplitz matrix inversion formula and rapid Toeplitz matrix-vector multiplications are utilized to lower the computational costs. For convergence analysis, a sufficient condition is established to guarantee that the error bound is independent of the norm of the matrix. Numerical results are given to demonstrate the efficiency of the method.