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Which of the following methods is surely convergent?

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Important Questions on Numerical Methods

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Mathematics>Mathematics and Computation>Numerical Methods>Numerical Solution of Equation
One root of the equation, x3-3x-5=0 lies between 2 and 2.5. Using Newton-Raphson method, the value of that root will be
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Mathematics>Mathematics and Computation>Numerical Methods>Numerical Solution of Equation
One root of the equation x3−4x+1=0 is between 1 and 2. The value of this root using Newton-Raphson method will be
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Mathematics>Mathematics and Computation>Numerical Methods>Numerical Solution of Equation
For the solution of equation f(x)=0 by the Newton-Raphson method, the value of x tends to root of the equation highly when f'xn is
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Mathematics>Mathematics and Computation>Numerical Methods>Numerical Solution of Equation
The 2nd approximation to a root of the equation x2-x-1=0 in the interval 1,2 by Bisection method will be:
HARD
Mathematics>Mathematics and Computation>Numerical Methods>Numerical Solution of Equation
If f0=3, f1=5, f3=21, then the unique polynomial of degree 2 or less using Newton divided difference interpolation will be: 
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Mathematics>Mathematics and Computation>Numerical Methods>Numerical Solution of Equation
By Bisection method, the real root of the equation x3-9x+1=0 lying between x=2 and x=4 is nearer to
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Mathematics>Mathematics and Computation>Numerical Methods>Numerical Solution of Equation
In solving ordinary differential equation y'=2x, y0=0 using Euler's method, the iterate yn, n∈N satisfy
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Mathematics>Mathematics and Computation>Numerical Methods>Numerical Solution of Equation
The value of 12 upto three places of decimals using the method of Newton-Raphson, will be
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Mathematics>Mathematics and Computation>Numerical Methods>Numerical Solution of Equation
The iteration formula xn+1=xn-fxnf'xn is commonly known as
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Mathematics>Mathematics and Computation>Numerical Methods>Numerical Solution of Equation
Performing 3 iterations of bisection method the smallest positive approximate root of the emation x3-5x+1=0 is
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Mathematics>Mathematics and Computation>Numerical Methods>Numerical Solution of Equation
By Newton-Raphson method, the positive root of the equation x4-x-10=0 is
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Mathematics>Mathematics and Computation>Numerical Methods>Numerical Solution of Equation
The bisection method is applied to compute a zero of the function fx=x4-x3-x2-4 in the interval 1,9. The method converges to a solution after _____ iterations.
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Mathematics>Mathematics and Computation>Numerical Methods>Numerical Solution of Equation
If one root of the equation fx=0 is near to x0, then the first approximation of this root as calculated by Newton Raphson method is the abscissa of the point, where the following straight line intersects the x-axis"
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Mathematics>Mathematics and Computation>Numerical Methods>Numerical Solution of Equation
If a and a+h are two consecutive approximate roots of the equation fx=0 as obtained by Newtons Method, then h is equal to
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Mathematics>Mathematics and Computation>Numerical Methods>Numerical Solution of Equation
One real root of a polynomial Px=x3-x-1 lies in the interval 1,2 and bisection method is used to find its value, the minimum number of interations required to achieve accuracy up to two decimal points is
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Mathematics>Mathematics and Computation>Numerical Methods>Numerical Solution of Equation
The formula for obtaining real root of an equation fx=0 in a given interval by Regula Falsi method, is
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Mathematics>Mathematics and Computation>Numerical Methods>Numerical Solution of Equation
The Newton Raphson method converges fast, if f'(α) is
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Mathematics>Mathematics and Computation>Numerical Methods>Numerical Solution of Equation
If fx=x2, then the second order divided difference for the points x0,x1,x2 will be:
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Mathematics>Mathematics and Computation>Numerical Methods>Numerical Solution of Equation
According to Newton-Raphson method, the value of 12 upto three places of decimal will be
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Mathematics>Mathematics and Computation>Numerical Methods>Numerical Solution of Equation
The per-unit power output of a salient-pole generator which is connected to an infinite bus, is given by the expression, P=1.4 sinδ+0.15sin2δ, where δ is the load angle. Newton-Raphson method is used to calculate the value of δ for P=0.8 pu. If the initial guess is 30°, then its value (in degree) at the end of the first iteration is