计算大型对称正定Toeplitz矩阵最小特征值的不精确Newton法  

INEXACT NEWTON METHOD FOR COMPUTING THE SMALLEST EIGENVALUE OF LARGE SYMMETRIC POSITIVE DEFINITE TOEPLITZ MATRIX

作　　者：黄丽萍[1] 

机构地区：[1]南京航空航天大学数学系,南京210016

出　　处：《高等学校计算数学学报》2013年第4期362-374,共13页Numerical Mathematics A Journal of Chinese Universities

摘　　要：Toeplitz矩阵是数学和应用科学中具有广泛应用的特殊矩阵之一．Inexact Newton method is an effective method for solving large sym- metric eigenvalue problems, which can reach superlinear convergence in proper condition. Applying the asymptotic behavior of eigenvalues between Toeplitz and its approximate circulant matrices~ the smallest eigenvalue of the approximate cir- culant matrix can be used as the initial guess of the inexact Newton method . Combining with the fast Fourier transform, a new inexact Newton method for computing the smallest eigenvalue of large symmetric positive definite Toeplitz ma- trices is presented. For the clustered eigenvalues, a preconditioned inexact Newton method is developed based on the sine-transform to speed up the convergence. Nu- merical results show that the proposed methods are efficient.

关 键 词：TOEPLITZ矩阵 不精确NEWTON法 最小特征值 对称正定 计算 应用科学 特殊矩阵 数学 

分 类 号：O241.6[理学—计算数学]