Computing Simple Roots by an Optimal Sixteenth-Order Class

Table 1

Test functions and their zeros.

Nonlinear functions	Zeros
𝑓1(𝑥)=√𝑥^4+8sin(𝜋/(𝑥^2+2))+𝑥^3/(𝑥^4+1)−√6+8/17	𝑟1=−2
𝑓2(𝑥)=√𝑥^2+2𝑥+5−2sin(𝑥)−𝑥^2+3	𝑟2≈2.331967655883964
𝑓3(𝑥)=sin(𝑥)−𝑥/100	𝑟3=0
𝑓4(𝑥)=(1/3)𝑥^4−𝑥^2−(1/3)𝑥+1	𝑟4=1
𝑓5(𝑥)=𝑒^sin(𝑥)−1−𝑥/5	𝑟5=0
𝑓6(𝑥)=𝑥𝑒^𝑥2−(sin(𝑥))^2+3cos(𝑥)+5	𝑟6≈−1.207647827130919
𝑓7(𝑥)=𝑒^−𝑥+cos(𝑥)	𝑟7≈1.746139530408013
𝑓8(𝑥)=𝑥^4+sin(𝜋/(𝑥^2))−5	𝑟8=√2
𝑓9(𝑥)=10𝑥𝑒^−𝑥2−1	𝑟9≈1.679630610428450
𝑓10(𝑥)=𝑥^3+4𝑥^2−15	𝑟10≈1.631980805566063