- Access to
**2 Million+**Textbook solutions - Ask any question from
**24/7**available

Tutors

a. Show that the LU Factorization Algorithm requires

1/3 n3 - 1/3 n multiplications/divisions and 1/3 n3 - 1/2 n2 + 1/6 n additions/subtractions

b. Show that solving Ly = b, where L is a lower-triangular matrix with lii = 1 for all i, requires

1/2 n2 - 1/2 n multiplications/divisions and 1/2 n2 - 1/2 n additions/subtractions

c. Show that solving Ax = b by first factoring A into A = LU and then solving Ly = b and Ux = y requires the same number of operations as the Gaussian Elimination Algorithm 6.1.

d. Count the number of operations required to solve m linear systems Ax(k) = b(k) for k =1, . . . ,m by first factoring A and then using the method of part (c) m times.

1/3 n3 - 1/3 n multiplications/divisions and 1/3 n3 - 1/2 n2 + 1/6 n additions/subtractions

b. Show that solving Ly = b, where L is a lower-triangular matrix with lii = 1 for all i, requires

1/2 n2 - 1/2 n multiplications/divisions and 1/2 n2 - 1/2 n additions/subtractions

c. Show that solving Ax = b by first factoring A into A = LU and then solving Ly = b and Ux = y requires the same number of operations as the Gaussian Elimination Algorithm 6.1.

d. Count the number of operations required to solve m linear systems Ax(k) = b(k) for k =1, . . . ,m by first factoring A and then using the method of part (c) m times.

- Access to
**2 Million+**Textbook solutions - Ask any question from
**24/7**available

Tutors

Get help from** Numerical Analysis **Tutors

Ask questions directly from** Qualified Online Numerical Analysis Tutors **.

Best for online homework instance.