Final answer:
Statement (d) 'The Golden Section search reduces the interval faster than the Bisection method' is not correct because the Bisection method halves the interval on each iteration, while the Golden Section method reduces it by a factor related to the golden ratio, which does not equate to a faster reduction per iteration.
Step-by-step explanation:
The statement that is not correct regarding the Bisection search and Golden Section search methods is an option (d): 'The Golden Section search reduces the interval faster than the Bisection method.' Here's why each other statement is correct:
- (a) The number of iterations in both methods is indeed affected by the size of the initial interval as a larger interval generally requires more iterations to narrow down to the root or optimum point.
- (b) The relative error of both methods depends on the search interval since the precision of the found solution improves as the interval size decreases.
- (c) Both methods require an initial interval containing the root or optima to start the search. This interval is systematically reduced to close in on the root or optimal value.
However, statement (d) is not correct because the Golden Section search method does not necessarily reduce the interval faster than the Bisection method. The Bisection method halves the interval during each iteration, while the Golden Section search reduces the interval by a factor related to the golden ratio (approximately 1.618). The rate at which the interval is reduced in the Golden Section search does not surpass the consistent 50% reduction achieved by the Bisection method per iteration.