PYQs Based Test - 26 : Numerical Methods (Algebraic Equations)

If y = 2x³ – 3x² + 3x – 10, the value of Δ³y will be (where, Δ is forward differences operator)

The quadratic equation $x^2-4x+4=0$ is to be solved numerically, starting with the initial guess

X₀ = 3. The Newton-Raphson method is applied once to get a new estimate and then the Secant method is applied once using the initial guess and this new estimate. The estimated value of the root after the application of the Secant method is _______________.

Only one of the real roots of f(x) = x⁶ – x – 1 lies in the interval 1 ≤ x ≤ 2 and bisection method is used to find its value. For achieving an accuracy of 0.001, the required minimum number of iterations is __________.

The number of purely real elements in a lower triangular representation of the given 3 × 3 matrix obtained through the given decomposition is _____

≤ft[ {*20c 2&3&3\\ 3&2&1\\ 3&1&7 } ] = ≤ft[ {*20c {a_11}&0&0\\ {a_12}&{a_22}&0\\ {a_13}&{a_23}&{a_33} } ]{≤ft[ {*20c {a_11}&0&0\\ {a_12}&{a_22}&0\\ {a_13}&{a_23}&{a_33} } ]^T}

In the Newton-Raphson method, an initial guess of x₀ = 2 is made and the sequence x₀ , x₁ , x₂ …

is obtained for the function

0.75x³ – 2x² – 2x + 4 = 0

Consider the statements

(I) x₃ = 0.

(II) The method converges to a solution in a finite number of iterations.

Which of the following is TRUE?