Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices
نویسندگان
چکیده
منابع مشابه
Computing Eigenelements of Real Symmetric Matrices via Optimization
In certain circumstances, it is more advantageous to use an optimization approach in order to solve the generalized eigenproblem Ax = Bx, where A and B are real symmetric matrices and B is positive deenite. This is the case namely when the matrices A and B are very large and the computational cost of solving, with high accuracy, systems of equations involving these matrices is prohibitive. The ...
متن کاملEstimation of uTƒ(A)v for large-scale unsymmetric matrices
Fast algorithms, based on the unsymmetric look-ahead Lanczos and the Arnoldi process, are developed for the estimation of the functional (f)= uf(A)v for xed u; v and A, where A∈Rn×n is a large7 scale unsymmetric matrix. Numerical results are presented which validate the comparable accuracy of both approaches. Although the Arnoldi process reaches convergence more quickly in some cases, it 9 has ...
متن کاملEstimation of uTf(A)v for large-scale unsymmetric matrices
Fast algorithms, based on the unsymmetric look-ahead Lanczos and the Arnoldi process, are developed for the estimation of the functional (f)= uf(A)v for xed u; v and A, where A∈Rn×n is a largescale unsymmetric matrix. Numerical results are presented which validate the comparable accuracy of both approaches. Although the Arnoldi process reaches convergence more quickly in some cases, it has grea...
متن کاملA restarted Induced Dimension Reduction method to approximate eigenpairs of large unsymmetric matrices
Background • The IDR(s) was introduced for solving linear systems in [3]. • IDR(s) creates residual vectors in the nested and shrinking subspaces Gj defined as Gj ≡ (A− μjI)(Gj−1 ∩ P⊥) j = 1, 2, . . . where P ∈ Cn×s and G0 ≡ C; in order to extract the approximated solution. • First IDR(s) method to solve Eq. (1) was proposed by M. H. Gutknecht and J.-P. M. Zemke [2]. The work we present here is...
متن کاملA mathematically simple method based on denition for computing eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices
In this paper, a fundamentally new method, based on the denition, is introduced for numerical computation of eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices. Some examples are provided to show the accuracy and reliability of the proposed method. It is shown that the proposed method gives other sequences than that of existing methods but they still are convergent to th...
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: Linear Algebra and its Applications
سال: 1980
ISSN: 0024-3795
DOI: 10.1016/0024-3795(80)90169-x