Use the Gauss elimination method to solve the system of equations:
$$ \begin{bmatrix} 1 & -2 & 1 & | & 0\\[4pt] 2 & 1 & -3 & | & 5\\[4pt] 4 & -7 & 1 & | & -1 \end{bmatrix} ______ ____ __________ ____ _____ ________ ________ _____.
_________ _________ ____ __________ ________ ______.
___ _________ ___ ______ ________ ____ ________ __________ __________.
__________ ____ ______ ___ ___ _________ __________ ____ ___ _____.
___ _______ ___ ________ ______.
________ ___ ______ _______ _______ ______ __________ ___ _____.
___ _________ __________ ________ ______ ______ ________ ________ ____ _________.
_____ _______ _____ ______ ______ _______ _____ __________ ________.
_____ _____ ____ _____ ___ ___ _________ _______ ______ ________ ______.
__________ _____ _____ __________ ___ ________ ___ __________ __________ __________.
________ ________ ________ _________ ________ __________ ___ _______ __________ __________ ___ ______.
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__________ _________ __________ ___ __________.
__________ __________ _________ ______ ________ ______ __________ _________ _________ _____ _________.
_______ ___.
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Use the bisection method in the interval [2,4] to calculate the root/s of the equation
up to three iterations. Calculate the absolute relative approximate error at each stage.
Using the trapezoidal rule, estimate the value of the integra and the true error.
What are the advantages and drawbacks of the bisection method?
Determine the first eight random numbers generated by using the linear congruential random number generator with a=c=7 and m=10. What is the period of this random number sequence.
Define true error and relative true error
Explain why one should not use higher order polynomial interpolation. What would be a preferable method of using information from several data points for interpolation?
In what way is the Newton-Raphson method more beneficial than the bisection method?