Computing the eigenvalue of smallest modulus and its corresponding eigneveclor of an irreducible nonsingular M-matrix A is considered, It is shown that if the entries of A are known with high relative accuracy, its ei...Computing the eigenvalue of smallest modulus and its corresponding eigneveclor of an irreducible nonsingular M-matrix A is considered, It is shown that if the entries of A are known with high relative accuracy, its eigenvalue of smallest modulus and each component of the corresponding eigenvector will be determined to much higher accuracy than the standard perturbation theory suggests. An algorithm is presented to compute them with a small componentwise backward error, which is consistent with the perturbation results.展开更多
文摘Computing the eigenvalue of smallest modulus and its corresponding eigneveclor of an irreducible nonsingular M-matrix A is considered, It is shown that if the entries of A are known with high relative accuracy, its eigenvalue of smallest modulus and each component of the corresponding eigenvector will be determined to much higher accuracy than the standard perturbation theory suggests. An algorithm is presented to compute them with a small componentwise backward error, which is consistent with the perturbation results.
