TY - JOUR
T1 - Palindromic quadratization and structure-preserving algorithm for palindromic matrix polynomials of even degree
AU - Huang, Tsung Ming
AU - Lin, Wen Wei
AU - Su, Wei Shuo
PY - 2011/8
Y1 - 2011/8
N2 - In this paper, we propose a palindromic quadratization approach, transforming a palindromic matrix polynomial of even degree to a palindromic quadratic pencil. Based on the (S + S-1)-transform and Patel's algorithm, the structure-preserving algorithm can then be applied to solve the corresponding palindromic quadratic eigenvalue problem. Numerical experiments show that the relative residuals for eigenpairs of palindromic polynomial eigenvalue problems computed by palindromic quadratized eigenvalue problems are better than those via palindromic linearized eigenvalue problems or polyeig in MATLAB.
AB - In this paper, we propose a palindromic quadratization approach, transforming a palindromic matrix polynomial of even degree to a palindromic quadratic pencil. Based on the (S + S-1)-transform and Patel's algorithm, the structure-preserving algorithm can then be applied to solve the corresponding palindromic quadratic eigenvalue problem. Numerical experiments show that the relative residuals for eigenpairs of palindromic polynomial eigenvalue problems computed by palindromic quadratized eigenvalue problems are better than those via palindromic linearized eigenvalue problems or polyeig in MATLAB.
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U2 - 10.1007/s00211-011-0370-7
DO - 10.1007/s00211-011-0370-7
M3 - Article
AN - SCOPUS:79960843614
SN - 0029-599X
VL - 118
SP - 713
EP - 735
JO - Numerische Mathematik
JF - Numerische Mathematik
IS - 4
ER -