A Family of Derivative-Free Methods with High Order of Convergence and Its Application to Nonsmooth Equations

Table 4

Numerical results for function 𝑓₁₂(𝑥).

𝑥0=2.8	SM		STM (to𝑙𝑢=10^−11)		M7		M7mod
	iter	error	iter	error	iter	error	iter	error
𝛼=3	1	0.44	1	7.14𝑒−3	1	0.17	1	7.54𝑒−5
	2	0.89	2	8.39𝑒−6	2	1.69𝑒−11	2	1.0𝑒−14
	⋮		3	1.17𝑒−11	3	0
	24	6.0𝑒−10	4	0
	25	0
|𝑥𝑘+1−𝑥𝑘|	6.0𝑒−10		1.17𝑒−11		1.69e-8		7.54𝑒−5
|𝑓(𝑥𝑘+1)|	0		0		0		6.93𝑒−14
ACOC	2.0009		1.9984		—		—
𝑥0=−2.8	iter	error	iter	error	iter	error	iter	error
𝛼=−3	>10^4		1	7.14𝑒−3	1	5.66𝑒−3	1	7.54𝑒−5
			2	8.39𝑒−6	2	4.41𝑒−3	2	1.0𝑒−14
			3	1.17𝑒−11	⋮
			4	0	4	2.74𝑒−10
					5	NaN
|𝑥𝑘+1−𝑥𝑘|			1.17𝑒−11		NaN		7.54𝑒−5
|𝑓(𝑥𝑘+1)|			0		NaN		6.93𝑒−14
ACOC			1.9984		—		—
𝑥0=−10	iter	error	iter	error	iter	error	iter	error
𝛼=−3	>10^4		1	2.45	1	0.70	1	7.98𝑒−2
			2	0.55	2	0.73	2	3.2𝑒−13
			⋮		⋮
			5	2.05𝑒−8	7	2.23𝑒−9
			6	0	8	NaN
|𝑥𝑘+1−𝑥𝑘|			2.05𝑒−8		NaN		7.98𝑒−2
|𝑓(𝑥𝑘+1)|			0		NaN		1.95𝑒−12
ACOC			1.9368		—		—