
Solution of Algebraic and Transcendental Equations 5-5
2. Bisection or Bolzano (Interval-halving)
method.
3. Newton–Raphson (Tangents) method.
4. Secants (Chords) method.
5. False position (Regula Falsi) method.
5.7.1 Fixed Point Iteration
(Successive Approximation)
Method
The word iterate means to do again or to repeat.
It is derived from the Latin word ‘iterum’ which
means ‘again’. The iterative method is a process in
which we start from an initial guess x
0
and compute
step-by-step approximations x
1
, x
2
, … of an unknown
solution of an equation of the form
f ( x) = 0 (5.3)
In general, iteration methods are easy to pro-
gram since ...