Question

The quadrature formula ???¹ f(x)dx = c?f(-1) + c?f(0) + c?f(1) is exact for all the polynomials of degree less than or equal to 2. Determine c?, c? and c?. Determine the coefficients in the quadrature formula ??²? x?¹/² f(x)dx = ?2h[w?f(0) + w?f(h) + w?f(2h)] such that the formula is exact for all polynomials of degree as high as possible. What is the degree of precision? Given the values of the function f(x) = ln x at x? = 2.0, x? = 2.2 and x? = 2.6, find the approximate value of f(2.0) using the method based on quadratic interpolation. Obtain an error bound. Perform one iteration of the Bairstow method to extract a quadratic factor x² + px + q from the polynomial x? + x³ + 2x² + x + 1. Find the deflated polynomial. Use the initial approximation (??, ??) = (0.45, 0.45).

          The quadrature formula ???¹ f(x)dx = c?f(-1) + c?f(0) + c?f(1) is exact for all the polynomials of degree less than or equal to 2. Determine c?, c? and c?. Determine the coefficients in the quadrature formula
??²? x?¹/² f(x)dx = ?2h[w?f(0) + w?f(h) + w?f(2h)]
such that the formula is exact for all polynomials of degree as high as possible. What is the degree of precision?
Given the values of the function f(x) = ln x at x? = 2.0, x? = 2.2 and x? = 2.6, find the approximate value of f(2.0) using the method based on quadratic interpolation. Obtain an error bound.
Perform one iteration of the Bairstow method to extract a quadratic factor x² + px + q from the polynomial x? + x³ + 2x² + x + 1. Find the deflated polynomial. Use the initial approximation (??, ??) = (0.45, 0.45).

The quadrature formula ???¹ f(x)dx = c?f(-1) + c?f(0) + c?f(1) is exact for all the polynomials of degree less than or equal to 2. Determine c?, c? and c?. Determine the coefficients in the quadrature formula
??²? x?¹/² f(x)dx = ?2h[w?f(0) + w?f(h) + w?f(2h)]
such that the formula is exact for all polynomials of degree as high as possible. What is the degree of precision?
Given the values of the function f(x) = ln x at x? = 2.0, x? = 2.2 and x? = 2.6, find the approximate value of f(2.0) using the method based on quadratic interpolation. Obtain an error bound.
Perform one iteration of the Bairstow method to extract a quadratic factor x² + px + q from the polynomial x? + x³ + 2x² + x + 1. Find the deflated polynomial. Use the initial approximation (??, ??) = (0.45, 0.45).

Added by Gina G.

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