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Quantitative Methods
2 Find the root of the equation xex = cosx in the interval (0, 1) using
Regula-Falsi method correct to four decimal places.
Regula-Falsi method correct to four decimal places.
Quantitative Methods
1 Find a real root of the equation 3x + sinx − e
x = 0 by the method of
false position correct to four decimal places.
x = 0 by the method of
false position correct to four decimal places.
Quantitative Methods
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
2x^4+13x^3+29x^2+27x+9=0
Quantitative Methods
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
2x^4+13x^3+29x^2+27x+9=0
Quantitative Methods
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.
the Berge -Vieta method. Perform two iterations of the method.
Quantitative Methods
Determine the maximum error in quadratic interpolation at equispaced points ?
Quantitative Methods
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 ?
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 ?
Quantitative Methods
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 ?
3x₁ - x₄ = 1
4x₁ - x₂ + x₃ = 4
x₁ + 2x₃ = 1
-x₁ - x₂ - x₄ = 2
Further, determine whether the method converges or not ?
Quantitative Methods
) 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.
Quantitative Methods
(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).
polynomials T0(x), T1(x), T2(x), T3(x), and T4(x).
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