Q21GATE 2006MCQ

Match the following iterative methods for solving algebraic equations and their orders of convergence.

\begin{array}{|l|l|l|l|} \hline & \text { Method } & & \text { Order of Convergence } \\ \hline \text { 1. } & \text { Bisection } & \text { P. } & \text { 2 or more } \\ \hline \text { 2. } & \text { Newton-Raphson } & \text { Q. } & 1.62 \\ \hline \text { 3. } & \text { Secant } & \text { R. } & 1 \\ \hline \text { 4. } & \text { Regula falsi } & \text { S. } & 1 \text { bit per iteration } \\ \hline \end{array}

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Q22GATE 2005MCQ

If the trapezoidal method is used to evaluate the integral obtained $\int_{0}^{1} x^2dx$ , then the value obtained

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Q23GATE 2004MCQ

Consider the following iterative root finding methods and convergence properties: The correct matching of the methods and properties is

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Q24GATE 2004MCQ

If f(l) = 2, f(2) = 4 and f(4) = 16, what is the value of f(3) using Lagrange's interpolation formula?

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Q25GATE 2003MCQ

A piecewise linear function f (x) is plotted using thick solid lines in the figure below (the plot is drawn to scale). If we use the Newton-Raphson method to find the roots of f(x) = 0 using x0, x1 and x2 respectively as initial guesses, the roots obtained would be

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Q26GATE 2002MCQ

The trapezoidal rule for integration gives exact result when the integrand is a polynomial of degree

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Q27GATE 2002MCQ

The Newton-Raphson iteration $X_{n+1}=(X_{n}/2)+(3/(2X_{n}))$ can be used to solve the equation

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Q28MCQ

X, Y and Z are closed intervals of unit length on the real line. The overlap of X and Y is half a unit. The overlap of Y and Z is also half a unit. Let the overlap of X and Z be k units. Which of the following is true?

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Q29MCQ

The Newton-Raphson method is to be used to find the root of the equation $f(x)=0$ where $x_o$ is the initial approximation and $f'$ is the derivative of $f$ . The method converges

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Q30MCQ

Which of the following statements applies to the bisection method used for finding roots of functions:

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Q31MCQ

The trapezoidal method to numerically obtain $\int_a^b f(x) dx$ has an error $E$ bounded by $\frac{b-a}{12} h^2 \max f''(x), x \in [a, b]$ where $h$ is the width of the trapezoids. The minimum number of trapezoids guaranteed to ensure $E \leq 10^{-4}$ in computing $\ln 7$ using $f=\frac{1}{x}$ is

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Q32MCQ

The Newton-Raphson method is used to find the root of the equation $X^{2-}2=0$ . If the iterations are started from -1, the iterations will

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Q33MCQ

Using the forward Euler method to solve $y''(t) = f(t), y'(0)=0$ with a step size of $h$ , we obtain the following values of $y$ in the first four iterations:

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Q34MCQ

Newton-Raphson iteration formula for finding $\sqrt[3]{c}$ , where c > 0 is

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Q35MCQ

The iteration formula to find the square root of a positive real number b using the Newton Raphson method is

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Q36MSQ

Simpson's rule for integration gives exact result when f(x) is a polynomial of degree

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Q37MCQ

The simplex method is so named because

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Q38MCQ

Which of the following statements is true in respect of the convergence of the Newton-Rephson procedure?

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