Chapter 2

Question 1

Jacobi Iterative Formula

Answer 1

x(k+1) = D^(-1)(L+U)x(k) + D^(-1)b

Question 2

Jacobi Iteration Matrix

Answer 2

Tj = D^(-1)(L+U)

Question 3

Gauss - Siedel Iterative Formula

Answer 3

x(k+1) = (D-L)^(-1)Ux(k) + (D-L)^(-1)b

Question 4

Gauss-Siedel Iteration Matrix

Answer 4

Tgs = (D-L)^(-1) U

Question 5

SOR Iterative formula

Answer 5

x(k+1) = (D-wL)^(-1) ((1-w)D+wU)x(k) + (D-wL)^-1)b

Question 6

SOR Iteration Matrix

Answer 6

Tsor = (D-wL)^(-1)[(1-w)D +wU]

Question 7

Spectral radius of Tsor

Answer 7

p(Tsor)>= |1-w|

Question 8

Convergence

Answer 8

p(B)<1 => ||B||<1

Question 9

Limit of a sequence

Answer 9

If limit of |x(k) - x| = 0 as k tends to infinity then the limit of x(k) = x