A Fast Algorithm for Computing Pseudospectra of Companion Matrices
نویسندگان
چکیده
The concept of pseudospectra was introduced by Trefethen during the 1990s and became a popular tool to explain the behavior of non-normal matrices. It is well known that the zeros of a polynomial are equal to the eigenvalues of the associated companion matrix. It is feasible to do the sensitivity analysis of the zeros of polynomials by the tool of pseudospectra of companion matrices. Thus, the pseudospectra problem of companion matrices is meaningful. In this paper, we propose a fast algorithm for computing the pseudospectra of companion matrices by using fast QR factorization. At last, numerical experiments and comparisons are given to illustrate(confirm) the efficiency of the new algorithm. Keywords-Pseudospectra; Companion matrix; Grid; SVD; QR factorization; Field of values; Gershgorin disk
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