Advances in Operations Research

Research Article

A Trust-Region-Based BFGS Method with Line Search Technique for Symmetric Nonlinear Equations

Table 1

Test Results For Problem 1.

(a) (Small-scales). Test results for Algorithm 2.1.


x0	(1,,1)	(60,,60)	(600,,600)

Dim	NI/NG/EG	NI/NG/EG	NI/NG/EG	NI/NG/EG	NI/NG/EG	NI/NG/EG
	13/24/2.406624e-07	14/25/2.272840e-07	17/30/3.104130e-07	13/24/2.449361e-07	14/25/2.398188e-07	17/30/4.593832e-07
	48/101/2.189696e-07	49/102/4.009098e-07	50/103/2.147571e-07	48/101/2.181267e-07	49/102/4.008911e-07	50/103/2.120250e-07
	82/171/6.794811e-07	89/188/6.345939e-07	91/190/7.804790e-07	82/171/8.358725e-07	89/188/6.367964e-07	91/190/7.801889e-07

x0	(1,0,1,0,)	(60,0,60,0,)	(600,0,600,0,)

Dim	NI/NG/EG	NI/NG/EG	NI/NG/EG	NI/NG/EG	NI/NG/EG	NI/NG/EG
	21/42/7.364467e-07	22/43/3.922363e-07	22/45/4.894966e-07	21/44/3.463471e-08	22/43/3.860638e-07	22/45/4.895404e-07
	72/153/9.350290e-07	86/181/4.420131e-07	88/185/7.620218e-07	70/151/6.776281e-07	86/181/4.420083e-07	49/83/8.003368e-07
	73/156/9.013346e-07	88/185/7.631881e-07	88/191/6.856481e-07	74/161/9.918464e-07	88/185/7.368909e-07	88/191/6.856897e-07

(b) (Large-scales). Test results for Algorithm 2.1.


x0	(1,,1)	(60,,60)	(600,,600)

Dim	NI/NG/EG	NI/NG/EG	NI/NG/EG	NI/NG/EG	NI/NG/EG	NI/NG/EG
	83/178/9.096568e-7	106/225/9.483206e-7	117/250/8.796828e-7	85/180/7.376219e-7	106/225/9.263058e-7	117/250/8.779599e-7
	85/180/8.830573e-7	103/218/9.825658e-7	115/244/9.765194e-7	83/178/7.659650e-7	103/218/9.796118e-7	115/244/9.755827e-7
	76/165/8.611337e-7	96/207/8.301215e-7	105/224/9.957816e-7	76/165/8.587066e-7	96/207/8.291876e-7	105/224/9.925005e-7

x0	(1,0,1,0,)	(60,0,60,0,)	(600,0,600,0,)

Dim	NI/NG/EG	NI/NG/EG	NI/NG/EG	NI/NG/EG	NI/NG/EG	NI/NG/EG
	68/149/8.780047e-7	91/194/7.484521e-7	101/216/9.790557e-7	69/150/9.770900e-7	91/194/7.275693e-7	101/216/9.559911e-7
	72/155/9.797645e-07	96/205/9.993161e-7	106/225/8.916405e-7	72/155/9.886969e-7	97/206/7.492841e-7	106/225/8.921008e-7
	69/152/9.919863e-7	93/200/6.930976e-7	106/227/8.119328e-7	69/152/9.948500e-7	93/200/6.946308e-7	106/227/8.123102e-7

(c) (Small-scales). Test results for Algorithm 2.2.


x0	(1,,1)	(60,,60)	(600,,600)

Dim	NI/NG/EG	NI/NG/EG	NI/NG/EG	NI/NG/EG	NI/NG/EG	NI/NG/EG
	54/107/8.039519e-7	67/133/7.624248e-7	74/147/8.167466e-7	54/107/8.061366e-7	67/133/7.624560e-7	74/147/8.167469e-7
	58/115/9.602663e-7	72/143/7.684310e-007	79/157/8.876868e-7	58/115/9.603892e-7	72/143/7.684327e-007	79/157/8.876870e-7
	60/119/7.614838e-7	73/145/8.350445e-7	80/159/9.679851e-7	60/119/7.615091e-7	73/145/8.350450e-7	80/159/9.679851e-7

x0	(1,0,1,0,)	(60,0,60,0,)	(600,0,600,0,)

Dim	NI/NG/EG	NI/NG/EG	NI/NG/EG	NI/NG/EG	NI/NG/EG	NI/NG/EG
	52/103/7.605486e-7	64/127/9.929883e-7	72/143/7.732628e-7	52/103/7.646868e-7	64/127/9.930747e-7	72/143/7.732660e-7
	56/111/8.896898e-7	69/137/9.690007e-7	77/153/8.223484e-7	56/111/8.899175e-7	69/137/9.690048e-7	77/153/8.223488e-7
	57/113/9.598124e-7	71/141/7.734909e-7	78/155/8.965851e-7	57/113/9.598763e-7	71/141/7.734918e-7	78/155/8.965852e-7

(d) (Large-scales). Test results for Algorithm 2.2.


x0	(1,,1)	(60,,60)	(600,,600)

Dim	NI/NG/EG	NI/NG/EG	NI/NG/EG	NI/NG/EG	NI/NG/EG	NI/NG/EG
	61/121/8.110467e-7	74/147/8.917908e-7	82/163/7.610549e-7	61/121/8.110534e-7	74/147/8.917909e-7	82/163/7.610549e-7
	62/123/9.526492e-7	76/151/7.712044e-7	83/165/8.958279e-7	62/123/9.526504e-7	76/151/7.712044e-7	83/165/8.958279e-7
	63/125/9.938699e-7	77/153/8.049274e-7	84/167/9.351920e-7	63/125/9.938703e-7	77/153/8.049274e-7	84/167/9.351920e-7

x0	(1,0,1,0,)	(60,0,60,0,)	(600,0,600,0,)

Dim	NI/NG/EG	NI/NG/EG	NI/NG/EG	NI/NG/EG	NI/NG/EG	NI/NG/EG
	59/117/7.503172e-7	72/143/8.249912e-7	79/157/9.576414e-7	59/117/7.503296e-7	72/143/8.249914e-7	79/157/9.576414e-7
	60/119/8.811245e-7	73/145/9.701366e-7	81/161/8.285552e-7	60/119/8.811269e-7	73/145/9.701367e-7	81/161/8.285552e-7
	61/121/9.191890e-7	75/149/7.444393e-7	82/163/8.649128e-7	61/121/9.191896e-7	75/149/7.444393e-7	82/163/8.649128e-7