QUESTION 4 (10) (a) A natural cubic spline that fits the data given by f(3.0) =...
QUESTION 4 (10) (a) A natural cubic spline that fits the data given by 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) 2+y=9, 22 + y2 = 25, 2,y> 0. Perform one iteration of Newton's method to approximate the solution, starting with (2, 4) as the initial solution. [20]
QUESTION 4 (a) A natural cubic spline that fits the data given by 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 x2 + y = 9, 22 + y2 = 25, x, y > 0. Perform one iteration of Newton's method to approximate the solution, starting with (2, 4) as...
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,...
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,...
Question 3 (a) Grven that f(-2)= 46, f(-1) 4, J(1) 1, f(3)= 156, and f(4)= 484, formula to estimate f(0) Use four-decimal arithmetac with rounding use the Lagrange interpolation (8) (b) Why should the Lagrange formula be used in practice only with caution" (2) (e) Wnte down the system of equations that need to be solved in order Function for the following data to construct the natural cubic spline 30 -5 6790 -3 6674 3 1 32-22178 (8) Note You...
Design a MATLAB code to construct a natural cubic spline P(x) that passes though the points (1, 1), (4, 1/4), (7, 1/7), (10, 1/10), (13, 1/13) and (16, 1/16). (a) Use the constructed cubic spline to interpolate x = 3; (b) Find the error e_1 = |1/3 - P(3)|;
10-16 DETERMINATION OF SPLINES Find the cubic spline g(x) for the given data with ko and kn as given. using MATLAB. 15. fo f(O)4, fi = f(2) 0, f3f(6) 80, ko= k3 = 0 f2 f(4) 4 10-16 DETERMINATION OF SPLINES Find the cubic spline g(x) for the given data with ko and kn as given. using MATLAB. 15. fo f(O)4, fi = f(2) 0, f3f(6) 80, ko= k3 = 0 f2 f(4) 4
1. Fit cubic splines to the following data (1) using natural end condition and estimate f(4.0) with the cubic spline. (2) using clamped end condition with f1’=-2.5, f5’=3.0 and estimate f(4.0) with the cubic spline. (3) using “not-a-knot” end condition and estimate f(4.0) with the cubic spline. 4 2 9.0 7.0 5.0 2.5 1.0 Xi 2.5 0.5 2.5 1.0 fi 2,5 er 4 2 9.0 7.0 5.0 2.5 1.0 Xi 2.5 0.5 2.5 1.0 fi 2,5 er
(a) Given the (z, y) values (1, 2), (2, 4), (3, 10), (5,8) write in matrix form the linear system to solve for the b, coelicients in the interpolating cubic spline with natural boundary conditions. (b) If an interpolating cubic spline is as given below, find (1) what points it interpolates and (2) its value at z= 0. -1.27(r +1)3 + 6.54(r + 1) – 2 for -1 <r<1 9.15(r - 1)3 - 7.57(r - 1)? - 8.59( - 1)...
1. Given the data table with f(x) = yn for a unkown function f, determine the cubic spline interpolation that intersects with the 3 data points. No need to solve for the coefficients. Just set up the eight equations. 1.1 3.5 1.2 3.7 1.3 2.9 2. The fixed point iteration can be used to find the solution of a function f(r) = 0. To use this method, we need to first identify g(x) such that the solution of g(x) =...