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Numerical analysis Question 1 A clamped cubic spline Six) on interval [0, 2) is defined by...
2. Consider the cubic spline for a function f on [0, 2] defined by S(x) = { ={ (z. 2x3 + ax2 + rx +1 if 0 < x <1 (x - 1)3 + c(x - 1)2 + d(x - 1) + ß if 1 < x < 2 where r, c and d are constants. Find f'(0) and f'(2), if it is a clamped cubic spline.
beta is 1 2. ( 20p.) Consider the cubic spline for a function f on (0, 2) defined by 223 + ax2 + rx + 1 if 0 < x < 1 S(X) = (.x - 1)3 + c(x - 1)2 + d(x - 1) + B if i < x < 2 S(x) = { where r, c and d are constants. Find f'(0) and f'(2), if it is a clamped cubic spline.
Alpha=9 beta=3 yazarsin 2. ( 20p.) Consider the cubic spline for a function f on (0,2) defined by 2x3 + x² +rx +1 if 0 <x<1 S(x) = (x - 1)3 + c(x - 1)2 + d(x - 1) + B if 1<x<2 = {(2-1) where r,c and d are constants. Find f'(0) and f'(2), if it is a clamped cubic spline.
Question is highlighted, thank you! 2. On each interval I ]. i-0,..n 1, with length h, the cubic spline is given by Write down the (4n) conditions that determine the nat ural cubic spline and the clamped cubic spline. Recall. on each interval 1.-Fez,+1],に0.- n-1. with length h, the cubic spline is given by The equations which define a cubic spline (using the textbook's notation and that used in dass), that is the coefficients satisfy 41- 3h, and the c,...
Q8 Spline 15 Points Define s(2) = -5 + 8x6x2 + 2x2 on 1 < x <2, and 8(x) = 27 402 + 1822. on 2<< <3 Verify that s() is a cubic spline function on (1,3). Is it a natural spline function on this interval?
its a numerical analysis question QUESTION 4 (a) A natural cubic spline that fits the data given by (10) f(3.0) = -5.6790, f(3.1) = -3.6674, f(3.2) = -2.2178 is to be constructed. Write down explicitly the system of equations that need to be used to construct the required natural cubic spline. (b) Consider the nonlinear system (10) z+ y = 9, 1² + y2 = 25, 2, y > 0. Perform one iteration of Newton's method to approximate the solution,...
2. A natural cubic spline S is defined by S(z) = { $(") = 11 S. (C)=1+ B(-1) + D(x - 1)3 S (2)=1+b(-2) + 3(x - 2)2 + (x - 2) if 1 <3 <2 if 2 <3<3 Find B, D, b, and d. Hint: Recall that a natural cubic spline has S" equal to 0 at the endpoints.
Define the following functions, and verify if cubic splie on given interval, also determine if natural spline. on al Define: Sx) = -5+86-66x² + 2x3 12XL 2 land S(x) = 27-40x +18% - 2x² on. 22X<3 b) Verify that Sx) is a cubic spline function on 6 Is it a natural spline function on this interual?
Suppose that the function h is defined on the interval (-2, 2] as follows. -1 if -2<xs-1 0 if - 1<xs0 h(x) = 3 1 if 0<xs1 2 if 1<xs2 Find h(-1), h(0.25), and h (2). h (0.25) = | х ó ? h (2) = 0 Egnation Check Mac
pectively, 3. Ajoint pdf is defined by (C(x + 2y), for 0 <x< 2, and 0 < y< 1, fx.r(x,y) = -{-4** 0. otherwise. a. Find the value of C. b. Find the marginal pdf of X alone. 9 c. Find the pdf of U = U = x+132 4. Consider n independent rvs XX2, ..., X, having the same distribution with a common variance a?. For any i = 1,2, ..., n, find Cov(x,- 8, 8), where 8 =...