Rational QR-iteration without inversion
نویسندگان
چکیده
منابع مشابه
A rational QR-iteration
In this manuscript a new type of QR-iteration will be presented. Each step of this new iteration consists of two substeps. In the explicit version, first an RQ-factorization of the initial matrix A−κI = RQ will be computed, followed by a QR-factorization of the matrix (A−σI)QH . Applying the unitary similarity transformation defined by the QR-factorization of the transformed matrix (A−σI)QH , w...
متن کاملA Multishift Qr Iteration without Computation of the Shifts1
Each iteration of the multishift QR algorithm of Bai and Demmel requires the computation of a \shift vector" deened by m shifts of the origin of the spectrum that control the convergence of the process. A common choice of shifts consists of the eigenvalues of the trailing principal submatrix of order m, and current practice includes the computation of these eigenvalues in the determination of t...
متن کاملA stable iteration to the matrix inversion
The matrix inversion plays a signifcant role in engineering and sciences. Any nonsingular square matrix has a unique inverse which can readily be evaluated via numerical techniques such as direct methods, decomposition scheme, iterative methods, etc. In this research article, first of all an algorithm which has fourth order rate of convergency with conditional stability will be proposed. ...
متن کاملThe QR iteration method for quasiseparable matrices
Let {ak}, k = 1, . . . , N be a family of matrices of sizes rk × rk−1. For positive integers i, j, i > j define the operation aij as follows: a × ij = ai−1 · · ·aj+1 for i > j + 1, aj+1,j = Irj . Let {bk}, k = 1, . . . , N be a family of matrices of sizes rk−1 × rk. For positive integers i, j, j > i define the operation bij as follows: b × ij = bi+1 · · · bj−1 for j > i+ 1, bi,i+1 = Iri . It is...
متن کاملComputing Approximate (Symmetric Block) Rational Krylov Subspaces without Explicit Inversion
It has been shown that approximate extended Krylov subspaces can be computed –under certain assumptions– without any explicit inversion or system solves. Instead the necessary products A−1v are obtained in an implicit way retrieved from an enlarged Krylov subspace. In this paper this approach is generalized to rational Krylov subspaces, which contain besides poles at infinite and zero also fini...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Numerische Mathematik
سال: 2008
ISSN: 0029-599X,0945-3245
DOI: 10.1007/s00211-008-0177-3