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CSM258:NUMERICAL METHODS AND COMPUTATION:COS:3935

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If

f_i=10,\qquad f_{i-1}=7,\qquad f_{i-2}=5, f_i=10,\qquad f_{i-1}=7,\qquad f_{i-2}=5, what is the second backward difference? \nabla ^2 f_i=f_i-2f_{i-1}+f_{i-2}. \nabla ^2 f_i=f_i-2f_{i-1}+f_{i-2}.

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For the data

x=1,2,3,4,\qquad f(x)=1,8,27,64, x=1,2,3,4,\qquad f(x)=1,8,27,64, what is the first forward difference at x=1x=1?

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Which of the following is a first-order ordinary differential equation?

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Three distinct data points are given. What is the highest degree required for the unique polynomial passing through all three points?

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For the data

f_i=10,\qquad f_{i-1}=7, f_i=10,\qquad f_{i-1}=7, what is the first backward difference \nabla f_i\nabla f_i?

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The exact value of a quantity is 5050 and its approximation is 49.849.8. What is the relative error?

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Using the data

(1,2),\quad (2,3),\quad (4,7), (1,2),\quad (2,3),\quad (4,7), inverse interpolation is used to estimate xx when f(x)=5f(x)=5. Which quantity is constructed as the interpolation variable?

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For equally spaced data, the forward difference is defined by

\Delta f_i=f_{i+1}-f_i. \Delta f_i=f_{i+1}-f_i. If f_i=5f_i=5 and f_{i+1}=8f_{i+1}=8, what is \Delta f_i\Delta f_i?

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A quantity has exact value 2525 and approximate value 24.524.5. What is its percentage relative error?

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Which statement about a transcendental equation is correct?

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