An Arnoldi Method for Nonlinear Eigenvalue Problems
نویسندگان
چکیده
منابع مشابه
An Arnoldi Method for Nonlinear Eigenvalue Problems
For the nonlinear eigenvalue problem T (λ)x = 0 we propose an iterative projection method for computing a few eigenvalues close to a given parameter. The current search space is expanded by a generalization of the shift-and-invert Arnoldi method. The resulting projected eigenproblems of small dimension are solved by inverse iteration. The method is applied to a rational eigenvalue problem gover...
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where T (λ) ∈ R is a family of symmetric matrices depending on a parameter λ ∈ J , and J ⊂ R is an open interval which may be unbounded. As in the linear case T (λ) = λI −A a parameter λ is called an eigenvalue of T (·) if problem (1) has a nontrivial solution x 6= 0 which is called a corresponding eigenvector. We assume that the matrices T (λ) are large and sparse. For sparse linear eigenvalue...
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ژورنال
عنوان ژورنال: BIT Numerical Mathematics
سال: 2004
ISSN: 0006-3835
DOI: 10.1023/b:bitn.0000039424.56697.8b