Numerical Analysis: Define a spline function B(x) consisting polonimials of dere
ID: 3417363 • Letter: N
Question
Numerical Analysis:
Define a spline function B(x) consisting polonimials of deree 3 as follows:
Assume B(x) = B(-x) for all x, that is B(x) is symmetric about the y-axis
Show that B is a cubic spline of degree 3.
Professor's hint : this function is bell-shaped, and symmetric about y-axis. So just check on the right side of y-axis. Check the continuity of B(x), B'(x), B''(x) at interior points on the two consecutive splines B0 and B1.
Numerical Analysis: Define a spline function B(x) consisting polonimials of deree 3 as follows: B(x) = (2- x)^3 for 1 geq 2, Assume B(x) = B(-x) for all x, that is B(x) is symmetric about the y-axis Show that B is a cubic spline of degree 3. Professor's hint : this function is bell-shaped, and symmetric about y-axis. So just check on the right side of y-axis. Check the continuity of B(x), B'(x), B''(x) at interior points on the two consecutive splines B0 and B1. leq 1, B(x) = 0 for x leq x leq 2, B(x)= 1 + 3(1- x) + 3(1- x)2 -3(1- x)3 for 0 leq xExplanation / Answer
<p>Numerical Analysis:</p> <p>Define a spline function B(x) consisting polonimials of deree 3 as follows:</p> <p>B(x) = (2- x)<sup>3</sup> for 1<img alt="leq" src="https://latex.codecogs.com/gif.latex?%5Cleq" /> x <img alt="leq" src="https://latex.codecogs.com/gif.latex?%5Cleq" /> 2,</p> <p>B(x)= 1 + 3(1- x) + 3(1- x)<sup>2</sup> -3(1- x)<sup>3</sup> for 0 <img alt="leq" src="https://latex.codecogs.com/gif.latex?%5Cleq" /> x <img alt="leq" src="https://latex.codecogs.com/gif.latex?%5Cleq" /> 1,</p> <p>B(x) = 0 for x <img alt="geq" src="https://latex.codecogs.com/gif.latex?%5Cgeq" /> 2,</p> <p>Assume B(x) = B(-x) for all x, that is B(x) is symmetric about the y-axis</p> <p>Show that B is a cubic spline of degree 3.</p> <p>Professor's hint : this function is bell-shaped, and symmetric about y-axis. So just check on the right side of y-axis. Check the continuity of B(x), B'(x), B''(x) at interior points on the two consecutive splines B<sub>0</sub> and B<sub>1.</sub></p>
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