Inner deflation for symmetric tridiagonal matrices

نویسنده

  • I. S. Dhillon
چکیده

Suppose that one knows an accurate approximation to an eigenvalue of a real symmetric tridiagonal matrix. A variant of deflation by the Givens rotations is proposed in order to split off the approximated eigenvalue. Such a deflation can be used instead of inverse iteration to compute the corresponding eigenvector. © 2002 Elsevier Science Inc. All rights reserved.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On deflation for symmetric tridiagonal matrices

K.V. Fernando developed an efficient approach for computation of an eigenvector of a tridiagonal matrix corresponding to an approximate eigenvalue. We supplement Fernando’s method with deflation procedures by Givens rotations. These deflations can be used in the Lanczos process and instead of the inverse iteration.

متن کامل

Homotopy algorithm for the symmetric diagonal-plus-semiseparable eigenvalue problem

A dense symmetric matrix can be reduced into a similar diagonalplus-semiseparable one by means of orthogonal similarity transformations. This makes such a diagonal-plus-semiseparable representation a good alternative to the tridiagonal one when solving dense linear algebra problems. For symmetric tridiagonal matrices there have been developed different homotopy eigensolvers. We present a homoto...

متن کامل

Implementation of the Orthogonal QD Algorithm for Lower Tridiagonal Matrices

The orthogonal qd algorithm with shifts (oqds algorithm), proposed by von Matt, is an algorithm for computing the singular values of bidiagonal matrices. This algorithm is accurate in terms of relative error, and it is also applicable to general triangular matrices. In particular, for lower tridiagonal matrices, BLAS Level 2.5 routines are available in preprocessing stage for this algorithm. BL...

متن کامل

Convergence rates to deflation of simple shift strategies

The computation of eigenvalues of real symmetric tridiagonal matrices frequently proceeds by a sequence of QR steps with shifts. We introduce simple shift strategies, functions σ satisfying natural conditions, taking each n × n matrix T to a real number σ(T ). The strategy specifies the shift to be applied by the QR step at T . Rayleigh and Wilkinson’s are examples of simple shift strategies. W...

متن کامل

Updating the QR decomposition of block tridiagonal and block Hessenberg matrices generated by block Krylov space methods

For MinRes and SymmLQ it is essential to compute the QR decompositions of tridiagonal coefficient matrices gained in the Lanczos process. Likewise, for GMRes one has to find those of Hessenberg matrices. These QR decompositions are computed by an update scheme where in every step a single Givens rotation is constructed. Generalizing this approach we introduce a block-wise update scheme for the ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2001