Convergence properties of waveform relaxation‐newton method

Kiichi Urahama

Research output: Contribution to journalArticlepeer-review


This paper shows the following properties for the waveform relaxation‐Newton method: (1) the iterative solution converges uniformly and globally under the same condition as the convergence condition for the waveform relaxation method; (2) the waveform Newton method used in the inner loop of the iteration converges locally with the second‐order; (3) the waveform relaxation‐Newton method is slower in the convergence both globally and locally than the waveform relaxation method; (4) the time interval where the error monotone decreases is shorter in the waveform relaxation‐Newton method than in the waveform relaxation method; and (5) the convergence speed asymptotically approaches that of the waveform relaxation method.

Original languageEnglish
Pages (from-to)108-115
Number of pages8
JournalElectronics and Communications in Japan (Part III: Fundamental Electronic Science)
Issue number8
Publication statusPublished - 1989
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering


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