Chapter 2.2, Problem 4ES

Let f(x) = x⁴ + 3x² − 2. To solve f(x) = 0, the following four fixed-pint problems are proposed. Derive each fixed point method and compute p₁, p₂, p₃, and p₄. Which methods seem to be appropriate?

1. a. $x=\sqrt{\frac{2-x^4}{3}},p_0=1$
2. b. $x=\sqrt[4]{2-3x^2},p_0=1$
3. c. $x=\frac{2-x^4}{3x},p_0=1$
4. d. $x=\sqrt[3]{\frac{2-3x^2}{x}},p_0=1$