GATE MA topic:numerical-analysis PYQs & Answers — Page 2

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topic:numerical-analysis

Questions 11–20 of 41. Imported answers require independent review unless marked reviewed.

Topic practice 41 questionsPage 2 of 5

Let

be the two fixed points of the function

, where

. For

, let the sequence

be generated by the fixed point iteration

Which one of the following is/are correct?

Your answerSelect all correct options. You can choose more than one.

converges to

for any

converges to

for any

converges to

for any

converges to

for any

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Let

. If

is the interpolating polynomial of degree less than or equal to 4 for the data

then the value of

is ____________.

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For a fixed

, let

. If the value of

obtained by using the Trapezoidal rule is equal to

, then the value of

is __________ (rounded off to 2 decimal places).

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Consider the linear system

, where

and

. Suppose

, where

and

are lower triangular and upper triangular square matrices, respectively. Consider the following statements:

: If each element of the main diagonal of

is 1, then

: For any choice of the initial vector

, the Jacobi iterates

converge to the unique solution of the linear system

Then

Your answerChoose one option.

both

and

are TRUE

is FALSE and

is TRUE

is TRUE and

is FALSE

both

and

are FALSE

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For

, and

, let

be a three-point formula to approximate

for any differentiable function

and

for every polynomial

of degree less than or equal to 2 and for all

, then

Your answerSelect all correct options. You can choose more than one.

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Let

be a twice continuously differentiable function on

such that

and

for all

. Let

for some

. The Newton-Raphson method to compute

is given by

for an initial guess

for some

, then which of the following statements is/are correct?

Your answerSelect all correct options. You can choose more than one.

For every

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The real sequence generated by the iterate scheme

Your answerChoose one option.

converges to

, for all

converges to

, whenever

converges to

, whenever

diverges for any

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Consider the linear system of equations

with

Which of the following statements are TRUE?

Your answerSelect all correct options. You can choose more than one.

The Jacobi iterative matrix is

The Jacobi iterative method converges for any initial vector

The Gauss-Seidel iterative method converges for any initial vector

The spectral radius of the Jacobi iterative matrix is less than 1

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is a polynomial of degree 5 and

where

are distinct points in the interval

, then the value of

is ________.

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The first derivative of a function

is approximated by an interpolating polynomial of degree 2, using the data

and

. It is found that

. Then, the value of

Your answerChoose one option.

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GATE MA topic:numerical-analysis PYQs

Question 52

Question 28

Question 29

Question 40

Question 50

Question 51

Question 18

Question 25

Question 30

Question 44