Quantitative Methods Answers

2 Find the root of the equation xex = cosx in the interval (0, 1) using
Regula-Falsi method correct to four decimal places.

1 Find a real root of the equation 3x + sinx − e
x = 0 by the method of
false position correct to four decimal places.

find the roots using simple fixed iteration. Stop until at 15th iteration or when approximate percent relative error is below 0.05%.

2x^4+13x^3+29x^2+27x+9=0

find the roots using newton raphson. Stop until at 15th iteration or when approximate percent relative error is below 0.05%.

2x^4+13x^3+29x^2+27x+9=0

Find a root of the equation 3x³+10x² +10x+7 = 0 which is close to −2.0, using
the Berge -Vieta method. Perform two iterations of the method.

Determine the maximum error in quadratic interpolation at equispaced points ?

Perform iterations of Newton-Raphson method to approximate a root of the
equation f(x) = x⁴ - x³ + x - 1 = 0, until the roots at successive iterations are
closer than 10⁻⁵
. How many iterations do you need for this much accuracy ?

Set up the iteration method in matrix form for the following system of linear equations
3x₁ - x₄ = 1
4x₁ - x₂ + x₃ = 4
x₁ + 2x₃ = 1
-x₁ - x₂ - x₄ = 2

Further, determine whether the method converges or not ?

) Find the Chebyshev interpolating polynomial that attains the values 6, 1, 3, and 66 at the points −1, 0, 2 and 6. Reduce the polynomial to its natural form.

(a) Using the formula Tn(x) = cos(n cos−1 x), n ≥ 0, find the Chebyshev
polynomials T0(x), T1(x), T2(x), T3(x), and T4(x).