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To find a zero of a function Ax) = x'-3x-2 by the Newton-Raphson iteration, the sequence {p,}n=0 converges to a root p = -1 in a ( ) way. How many initial points are required to guess in Newton-Raphson slope algorithm for finding a zero of the function f(x)? ( ) Point out, respectively, one of the advantages and drawbacks of the bracketing method, Advantage: ( ); Drawback: ( ).

To find a zero of a function Ax) = x'-3x-2 by the Newton-Raphson iteration, the sequence {p,}n=0 converges to a root p = -1 in a ( ) way. How many initial points are required to guess in Newton-Raphson slope algorithm for finding a zero of the function f(x)? ( ) Point out, respectively, one of the advantages and drawbacks of the bracketing method, Advantage: ( ); Drawback: ( ).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1). To find a zero of a function Ax) = x²-3x-2 by the Newton-Raphson iteration, the sequence {p,,}n=0 converges to a root p = -1 in a ( ) way. 2). How many initial points are required to guess in Newton-Raphson slope algorithm for finding a zero of the function f(x)? ( ) 3). Point out, respectively, one of the advantages and drawbacks of the bracketing method, Advantage: ( ); Drawback: ( ). 4). In order to constitute a fourth-order polynomial P4(x), how many distinct data points (xk, Yk) are at least required through which P4(x) will pass ( ). 5). If the Gauss-Legendre rule is used for an exact integral of a cubic polynomial over interval [-2, 2], write out the node abscissas of the least number ( and the related weights ( ). 6). Suppose the integral interval is [a, b]. The step size for the simple trapezoidal rule is ), while the step size for the simple Simpson's % rule is ( ).
Transcribed Image Text:1). To find a zero of a function Ax) = x²-3x-2 by the Newton-Raphson iteration, the sequence {p,,}n=0 converges to a root p = -1 in a ( ) way. 2). How many initial points are required to guess in Newton-Raphson slope algorithm for finding a zero of the function f(x)? ( ) 3). Point out, respectively, one of the advantages and drawbacks of the bracketing method, Advantage: ( ); Drawback: ( ). 4). In order to constitute a fourth-order polynomial P4(x), how many distinct data points (xk, Yk) are at least required through which P4(x) will pass ( ). 5). If the Gauss-Legendre rule is used for an exact integral of a cubic polynomial over interval [-2, 2], write out the node abscissas of the least number ( and the related weights ( ). 6). Suppose the integral interval is [a, b]. The step size for the simple trapezoidal rule is ), while the step size for the simple Simpson's % rule is ( ).
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