Discussion on a paper by Harn C. Chen

✍ Scribed by Weiming Liu

• Publisher: John Wiley and Sons
• Year: 1994
• Tongue: English
• Weight: 59 KB
• Volume: 23
• Category: Article
• ISSN: 0098-8847
• DOI: 10.1002/eqe.4290230109

✦ Synopsis

In this paper', the author claimed development of an efficient numerical algorithm to solve the quadratic eigenvalue problems. However, such an algorithm was published by Zheng et a1.' more than three years ago. Comparing the two papers, apart from the sections 'Preserving orthogonality between trial vectors' and 'Numerical examples', and minor differences in notations, the derivation and resulting formulation in Reference 1 appear to be identical to those of Reference 2. Moreover, error analysis was discussed in detail in Reference 2 using the concepts of 'eigenvalue square matrix'. The numerical results presented by Chen (no definite numbers were given by the way) consisted only of symmetrical matrices although he noted that the method can be used in solving problems with nonsymmetrical matrices. In fact, a solved nonsymmetrical problem involving matrices generated from pseudo-random numbers was presented in Reference 2. Finally, the number of multiplications of the proposed algorithm was compared with the QR method and the iterative method of Gupta3 by Zheng et al.