Quantitative Methods Answers

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 ?

(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).

Using the starting value 2(1 + i ), solve

x4 − 5x3 + 20x2 − 40x + 60 = 0 by Newton-Raphson method, given that all the roots of the given equation are complex.

Usin the method of false position. Find the root of equation x^6 - x^4 - x^3 - 1 = 0

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


3x^4-8x^3-37x^2+2x+40

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


2x^5+x^4-2x-1=0

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


e^x+x=4

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


2x^5+x^4-2x-1=0