Question

Define the rate of convergence and find the rate of convergence for the secant method.​

Answer 1

Answer: Convergence of secant method: Definition: Say, where is the root of , , are the errors at n and (n+1) iterations and are the approximations of at , (n+1) iterations. If where is a constant, then the rate of convergence of the method by which is generated is p. Say and i.e the error in the n iteration in estimating .

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Answer 2

Answer:

Rate of convergence

Step-by-step explanation:

The rate of convergence for a convergent sequence describes how quickly the terms of the sequence converge to the limit.

Standard text books in numerical analysis state that the secant method is superlinear: the rate of convergence is set by the gold number. Nevertheless, this property holds only for simple roots. If the multiplicity of the root is larger than one, the convergence of the secant method becomes linear.