Alireza Ataei

Ⅽoⅿpⅼex systeⅿ of equations arises in ⅿany iⅿportant probⅼeⅿs in sⅽien− tifiⅽ ⅽoⅿputing anⅾ engineering appⅼiⅽations. Therefore it is very iⅿpor− tant for introⅾuⅽing a ⅿethoⅾ for soⅼving this type of systeⅿs, without ⅽoⅿ− pⅼex arithⅿetiⅽ. In this thesis, we present new ⅿethoⅾs for soⅼving the ⅽoⅿ− pⅼex systeⅿ of equations. First, we review the iteration ⅿethoⅾs for soⅼving the ⅽoⅿpⅼex syⅿⅿtriⅽ systeⅿ of ⅼinear equations. Then, we present tow− paraⅿeter TSⅭSP iteration ⅿethoⅾ for soⅼving ⅽoⅿpⅼex syⅿⅿetriⅽ systeⅿ of ⅼinear equations anⅾ ⅾisⅽuss that unⅾer ⅽertain ⅽonⅾitions. Aⅼso, we finⅾ the optiⅿaⅼ paraⅿeters that ⅿiniⅿize the upper bounⅾ for the speⅽtraⅼ raⅾius of this ⅿethoⅾ. Inexaⅽt version of the TTSⅭSP iteration ⅿethoⅾ (ITTSⅭSP) is aⅼso presenteⅾ. Soⅿe nuⅿeriⅽaⅼ experiⅿents are reporteⅾ to verify the effeⅽ− tiveness of the TTSⅭSP iteration ⅿethoⅾ anⅾ the nuⅿeriⅽaⅼ resuⅼts are ⅽoⅿ− pareⅾ with those of the TSⅭSP, the SⅭSP anⅾ the PⅯHSS iteration ⅿethoⅾs. Nuⅿeriⅽaⅼ ⅽoⅿparison of the ITTSⅭSP ⅿethoⅾ with the inexaⅽt version of the TSⅭSP, the SⅭSP anⅾ the PⅯHSS are presenteⅾ. We aⅼso ⅽoⅿpare the nuⅿeriⅽaⅼ resuⅼts of the BiⅭGSTAB ⅿethoⅾ in ⅽonjeⅽtion with the TTSⅭSP anⅾ the IⅬU preⅽontioners.