Numerical Analysis Project Due Thursday 2/1/2020 Solve one of the following questions. 1. Read Se...

Numerical Analysis Project Due Thursday 2/1/2020 Solve one of the following questions. 1. Read Section 7.4 pages 462-467 from the text book (The SOR Method), then solve the following questions (a) What is the SOR Method? (b) What is the relation between the SOR Method and Gauss-Seidel method? (c) Consider the following three-by-three system 41121 +212.22 +213.13 = bı, 02121 +22222 +22343 = 62, 03121 + 23212 + 433.23 = 63. Write the equations to find the new iteration from the old one. (d) The linear system Ax = b given by 4x1 - 2x2 + 0x3 = 8, -221 +6x2 – 523 = -29, 0.21 – 522 +11:03 = 43. has the solution (1, -2,3)', using the SOR method with w = 1.2 solve this system given that x") = (0,0,0). Given that the stopping condition is that x(k) - x(k-1) ||2 <0.001. Write the results in a table with the following formate, iteration number 21 22 23 (e) Find the Tsor and Csor such that x = TSORX + CSOR (f) Is the matrix A positive definite and tridiagonal? If yes find the optimal choice of w for the SOR method.