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(a) Given the (z, y) values (1, 2), (2, 4), (3, 10), (5,8) write in matrix...
2. On each interval I ]. i-0,..n 1, with length h, the cubic spline is given by Write down the (4...
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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,...
2. More on Cubic Splines Consider the data Xi : 1 2 3 4 Yi :...
2. More on Cubic Splines Consider the data Xi : 1 2 3 4 Yi : 18 27 64 a. Construct the cubic interpolant, i.e., find the cubic polynomial p that satisfies p(xi) = Yi, i = 1,2,3,4 and draw its graph. b. Construct the interpolating natural cubic spline and draw its graph. c. Comment on your results.
3x0+1x2 + ! 040-2 8] [3 11. The augmented matrix for the linear system of equations in the unknowns a, y, z has red...
3x0+1x2 + ! 040-2 8] [3 11. The augmented matrix for the linear system of equations in the unknowns a, y, z has reduced row,echelon form given by 1401 0 01 -2 The general solution to this syste is (D) x = 1, y =-2, z = 0 (E) No solution
3x0+1x2 + ! 040-2 8] [3 11. The augmented matrix for the linear system of equations in the unknowns a, y, z has reduced row,echelon form given by 1401...
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-d...
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...
Given the linear transformation T:RPR:T[(x, y, z)] = (4x+Z, -34 +2 ) and basis B4={(2,4,-1); (0,1,-2);...
Given the linear transformation T:RPR:T[(x, y, z)] = (4x+Z, -34 +2 ) and basis B4={(2,4,-1); (0,1,-2); (0,2,-2)} and B2 = {(-3,0);(-2,11} Find element Q13 of the transformation matrix
4. Solve the following system of linear equations using the inverse matrix method. 1 y =...
4. Solve the following system of linear equations using the inverse matrix method. 1 y = 1 2 , 3 2 -r- 1 5 4 a) x+y +z= 6 x-y-3z=-8 x+y- 2z=-6 b) Solve the following system of linear equations using Cramer's Rule. 5. 2 1 -X- 3 2 1 3 X+-y-1 5 4 y = 1 a) x+y+z= 6 x-y-3z=-8 x+y- 2z = -6 b)
4. Solve the following system of linear equations using the inverse matrix method. 1...
1. Given the data table with f(x) = yn for a unkown function f, determine the...
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) =...
3. (20 points) Denote u(ar, y) the steady-state temperature in a rectangle area 0 z 10,...
3. (20 points) Denote u(ar, y) the steady-state temperature in a rectangle area 0 z 10, 0yS 1. Find the temperature in the rectangle if the temperature on the up side is kept at 0°, the lower side at 10° while the temperature on the left side is S0)= sin(y) and the right side is insulated. Answer the following questions. (a) (10 points) Write the Dirichlet problem including the Laplace's equation in two dimensions and the boundary conditions. (b) (10...
8.) (10 Points) Given the contour diagram z = f(x,y). 2 1 2 3 4 -2...
8.) (10 Points) Given the contour diagram z = f(x,y). 2 1 2 3 4 -2 R a. Find i. f(-1,1) 11. a value of x for which f(x, 1) = 3 iii. a value of y for which f(0,y) = -2 b. The given graph has a local maximum value. At which point (x,y) does this occur? c. Determine the sign (positive or negative) of the following partial derivatives. i. (1,0) ii. fy(0,1)
(1 point) -1 -4 a. Given that V1 [ 2] and U2 --10 are eigenvectors of...
(1 point) -1 -4 a. Given that V1 [ 2] and U2 --10 are eigenvectors of the matrix _2] determine the corresponding eigenvalues. 4 11 = 12 = = -4x b. Find the solution to the linear system of differential equations x' y' satisfying the initial conditions x(0) = -3 and y(0) = 4. 4x – 2y x(t) = y(t) =
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,...
2. More on Cubic Splines Consider the data Xi : 1 2 3 4 Yi : 18 27 64 a. Construct the cubic interpolant, i.e., find the cubic polynomial p that satisfies p(xi) = Yi, i = 1,2,3,4 and draw its graph. b. Construct the interpolating natural cubic spline and draw its graph. c. Comment on your results.
3x0+1x2 + ! 040-2 8] [3 11. The augmented matrix for the linear system of equations in the unknowns a, y, z has reduced row,echelon form given by 1401 0 01 -2 The general solution to this syste is (D) x = 1, y =-2, z = 0 (E) No solution
3x0+1x2 + ! 040-2 8] [3 11. The augmented matrix for the linear system of equations in the unknowns a, y, z has reduced row,echelon form given by 1401...
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...
Given the linear transformation T:RPR:T[(x, y, z)] = (4x+Z, -34 +2 ) and basis B4={(2,4,-1); (0,1,-2); (0,2,-2)} and B2 = {(-3,0);(-2,11} Find element Q13 of the transformation matrix
4. Solve the following system of linear equations using the inverse matrix method. 1 y = 1 2 , 3 2 -r- 1 5 4 a) x+y +z= 6 x-y-3z=-8 x+y- 2z=-6 b) Solve the following system of linear equations using Cramer's Rule. 5. 2 1 -X- 3 2 1 3 X+-y-1 5 4 y = 1 a) x+y+z= 6 x-y-3z=-8 x+y- 2z = -6 b)
4. Solve the following system of linear equations using the inverse matrix method. 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) =...
3. (20 points) Denote u(ar, y) the steady-state temperature in a rectangle area 0 z 10, 0yS 1. Find the temperature in the rectangle if the temperature on the up side is kept at 0°, the lower side at 10° while the temperature on the left side is S0)= sin(y) and the right side is insulated. Answer the following questions. (a) (10 points) Write the Dirichlet problem including the Laplace's equation in two dimensions and the boundary conditions. (b) (10...
8.) (10 Points) Given the contour diagram z = f(x,y). 2 1 2 3 4 -2 R a. Find i. f(-1,1) 11. a value of x for which f(x, 1) = 3 iii. a value of y for which f(0,y) = -2 b. The given graph has a local maximum value. At which point (x,y) does this occur? c. Determine the sign (positive or negative) of the following partial derivatives. i. (1,0) ii. fy(0,1)
(1 point) -1 -4 a. Given that V1 [ 2] and U2 --10 are eigenvectors of the matrix _2] determine the corresponding eigenvalues. 4 11 = 12 = = -4x b. Find the solution to the linear system of differential equations x' y' satisfying the initial conditions x(0) = -3 and y(0) = 4. 4x – 2y x(t) = y(t) =
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