On modified interval repeated zoro symmetric single-step IRZSS1-5D procedure for bounding polynomial zeros simultaneously

• Main Authors: Mohammad Rusli, Syaida Fadhilah, Monsi, Mansor, Hassan, Nasruddin, Senu, Norazak, Ismail, Fudziah, Ibrahim, Zarina Bibi
• Format: Conference or Workshop Item
• Language: English
• Published: AIP Publishing LLC 2014
• Online Access: http://psasir.upm.edu.my/id/eprint/57354/1/On%20modified%20interval%20repeated%20zoro%20symmetric%20single-step%20IRZSS1-5D%20procedure%20for%20bounding%20polynomial%20zeros%20simultaneously.pdf; http://psasir.upm.edu.my/id/eprint/57354/
• Institution: Universiti Putra Malaysia

We present a new rapidly convergence procedure called the interval repeated zoro symmetric single-step IRZSS1-5D which is an extension of the procedures IZSS1-5D and IRSS1. Theoretical analysis shows that the rate of convergence of IRZSS1-5D is at least 3r + 2 (r ≥ 1), whereas the rates of convergence of IZSS1-5D and IRSS1 are at least five and 2r + 1 (r ≥ 1), respectively. With r = 1, the procedure IRZSS1-5D is identical to IZSS1-5D. The procedures IRSS1 and IZSS1-5D are the basic references for the establishment of IRZSS1-5D, where the forward-backward-forward (FBF) step of IZSS1-5D are repeated r times in IRZSS1-5D, so that some elements of FBF of IZSS1-5D can be saved and reused for the next inner iterations r = 2,3, … in IRZSS1-5D.