Global Convergence of a Modified Spectral Conjugate Gradient Method

Table 2

Comparison of efficiency with the other methods.

Function	Algorithm	Dim	GV	NI	NF	CT(s)
Kowalik and Osborne	mfr	4	—	—	—	—
	prp	4	8.9521𝑒−007	833	26191	1.2970
	mprp	4	9.9698𝑒−007	6235	35425	3.5940
	msprp	4	9.9560𝑒−007	7059	37976	4.9850
Broyden banded	mfr	6	8.9469𝑒−007	40	505	0.0780
	prp	6	8.4684𝑒−007	268	9640	0.4840
	mprp	6	8.9029𝑒−007	102	1319	0.0940
	msprp	6	9.3276𝑒−007	44	556	0.0940
Discrete boundary	mfr	6	9.1531𝑒−007	107	509	0.0780
	prp	6	7.8970𝑒−007	269	11449	0.4690
	mprp	6	8.28079𝑒−007	157	1473	0.0930
	msprp	6	9.9436𝑒−007	165	1471	0.1410
Variably dimensioned	mfr	8	7.3411𝑒−007	57	1233	0.1250
	prp	8	7.3411𝑒−007	113	7403	0.3290
	mprp	8	9.0900𝑒−007	69	1544	0.0780
	msprp	8	7.3411𝑒−007	57	1233	0.1100
Broyden tridiagonal	mfr	9	9.1815𝑒−007	129	2173	0.1250
	prp	9	6.4584𝑒−007	113	5915	0.2500
	mprp	9	7.3529𝑒−007	187	2967	0.1250
	msprp	9	9.2363𝑒−007	82	1304	0.1100
Linear-rank1	mfr	10	9.7462𝑒−007	84	3762	0.1720
	prp	10	4.5647𝑒−007	98	6765	0.2810
	mprp	10	6.9140𝑒−007	51	2216	0.0780
	msprp	10	6.6630𝑒−007	50	2162	0.1250
Linear-full rank	mfr	12	7.6919𝑒−007	9	36	0.0160
	prp	12	8.2507𝑒−007	47	1904	0.1090
	mprp	12	7.6919𝑒−007	9	36	0.0630
	msprp	12	7.6919𝑒−007	9	36	0.0150