Formula should satisfy a constant function and first degree f(x) =x if it is exact for linear polynomials
(b) Find ao and a such that the following quadrature formula is exact for linear polynomials (b) Find ao and a such that the following quadrature formula is exact for linear polynomials
A weighted Gauss quadrature formula for the weight function
is
(a) The formula is exact for
, what is
?
(b) Use this formula to approximate the integral (keep 9 decimal
places)
.
(c) Compute the error. (Note: The error is less than
.)
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Numerical Analysis:
a) The basic form of the Gaussian quadrature formula is The integration formula using two points can be made exact when a polynomial of order 3 is integrated. i) Determine the weights c, c2 and the points , 2 e-radz.16] (ii) By find using a change of variable use Gaussian Quadrature to 0
a) The basic form of the Gaussian quadrature formula is The integration formula using two points can be made exact when a polynomial of order...
Given the following quadrature formula: (x)dx = c0) + f(a) Find a 4 and 2 so that the quadrature formula has the highest degree of precision. Clearly, state its degree. ſrcade -
What is the order of the quadrature formula corresponding to the approximation .G (6- V6 (6+ V6 Hint: find the coefficients (bi, ci)i=1, ,s of this quadrature formula
What is the order of the quadrature formula corresponding to the approximation .G (6- V6 (6+ V6 Hint: find the coefficients (bi, ci)i=1, ,s of this quadrature formula
3. Recall that the three-point Gaassian quadrature rule is with and the corresponding weight are (A). Show that this Gaussian quadrature rule is exact for polynoinials 1,エ·エ2,?,24, X5. (B). Use the transform to write the corresponding Gaussian quadrature formula
Problem Six: Given two polynomials: g(x) = anx" + an-iz"-1 +--+ aix + ao Write a MATLAB function (name it polyadd) to add the two polynomials and returns a polynomial t(x) = g(x) + h(x), whether m = n, m < n or m > n. Polynomials are added by adding the coefficients of the terms with same power. Represent the polynomials as vectors of coefficients. Hence, the input to the function are the vectors: g=[an an-1 ao] and h=[am...
Use
a sum or difference formula to find the exact value of the
following
Use a sum or difference formula to find the exact value of the following. 271 410 21 41 sin + cos sin 5 15 15 COS 0 8 Х
5. (10 points) What is the order of the following quadrature formula called Neuton's rule given by the coefficients (bo.bi,b, bs) (1/8,3/8,3/8, 1/8) and (o,,2)-
Problem Six: Given two polynomials: g(x) = anx" + an-iz"-1 +--+ aix + ao Write a MATLAB function (name it polyadd) to add the two polynomials and returns a polynomial t(x) = g(x) + h(x), whether m = n, m < n or m > n. Polynomials are added by adding the coefficients of the terms with same power. Represent the polynomials as vectors of coefficients. Hence, the input to the function are the vectors: g=[an an-1 ao] and h=[am...
5. Find which of the following quadrature formulas are of the interpolatory type. Show your analysis. b) x)dx f(-1)+f().
5. Find which of the following quadrature formulas are of the interpolatory type. Show your analysis. b) x)dx f(-1)+f().