Crout€™s method factorizes where L is lower triangular and U is upper triangular with diagonal entries

(a) Formulas. Obtain formulas for Crout€™s method similar to (4).

(b) Examples. Solve Prob. 5 by Crout€™s method.

(c) Factor the following matrix by the Doolittle, Crout, and Cholesky methods. 

(d) Give the formulas for factoring a tridiagonal matrix by Crout€™s method.

(e) When can you obtain Crout€™s factorization from Doolittle€™s by transposition?
Data from Prob. 5

Show the factorization and solve by Doolittle€™s method.

   3x₁ +   9x₂ +   6x₃ =   4.6
18x₁ + 48x₂ + 39x₃ = 27.2
  9x₁ - 27x₂ + 42x₃  =    9.0

Transcribed Image Text:

-4 -4 25 4 4 24 2.