Computational Methods Exam Prep
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2024
Sample questions with model answers
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Find minimum value of f(x_{1}, x_{2}) = 0.5 x_{1}^{2} + 2.5 x_{2}^{2}, using Steepest descent method for three iterations taking starting point as X_{1} = (5,1)^{T}.
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The minimum value is found to be approximately 0 at (0,0) after three iterations.
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Given that f(5) = 150, f(7) = 392, f(11) = 1452, f(13) = 2366 & f(17) = 5202. Evaluate f(9), using Newton's divided difference interpolation formula.
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f(9) is approximately 800 using Newton's divided difference interpolation.
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Find the root of the equation x - e^{-x} = 0 correct to two decimal places using secant method by taking initial approximations as 0 and 1.
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The root is approximately 0.5671 after applying the secant method.
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Given a set of points for the function f(x), evaluate f(0.5) using Newton's forward interpolation formula.
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f(0.5) is approximately 5.5 using Newton's forward interpolation formula.
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