MODIFIKASI METODE HOUSEHOLDER TANPA TURUNAN KEDUA DENGAN ORDE KONVERGENSI OPTIMAL
DOI:
https://doi.org/10.25077/jmu.10.2.218-228.2021Abstract
Metode Householder merupakan metode iterasi berorde konvergensi tiga yang digunakan untuk menyelesaikan persamaan nonliner. Selain itu, metode Householder menggunakan tiga evaluasi fungsi pada setiap iterasinya dengan indeks efisiensi sebesar 31/3 ≈ 1, 4422. Artikel ini membahas modifikasi metode Householder berparameter real λ menggunakan deret Taylor orde dua. Selanjutnya, turunan kedua direduksi menggunakan deret Taylor orde dua dan menambahkan satu parameter real θ. Hasil kajian menunjukkan bahwa metode iterasi baru mempunyai orde konvergensi empat untuk λ = 1 dan θ = 1 dan melibatkan tiga evaluasi fungsi dengan indeks efisiensinya sebesar 41/3 ≈ 1.5874. Simulasi numerik diberikan untuk menguji performasi metode iterasi tersebut yang meliputi jumlah iterasi dan nilai mutlak fungsi dengan menggunakan enam fungsi real. Ukuran-ukuran performasi dari metode iterasi baru dibandingkan dengan metode Newton, metode Newton-Steffensen, metode Householder dan metode Newton Ganda. Hasil simulasi numerik menujukkan bahwa metode iterasi baru mempunyai performasi yang lebih baik dibandingkan dengan metode iterasi lainnya.
Kata Kunci: Indeks efisiensi, metode Householder, orde konvergensi, persamaan nonlinier, simulasi numerik
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