Consider

the system of linear equations

a)

Solve the system using Gaussian elimination with partial pivoting.

b)

Solve the system using Gaussian elimination with complete pivoting.

c)

Determine the D, L, and U matrices of the Gauss-Seidel method

(equation

(6.19), page 280) and determine the spectral radius of

d) Do

three steps of the Gauss-Seidel method using the original formulation (6.57),

and starting with x(0) = (1, 1, 1), and evaluate

»

Consider

the system of linear equations

a)

Solve the system using Gaussian elimination with partial pivoting.

b)

Solve the system using Gaussian elimination with complete pivoting.

c)

Determine the D, L, and U matrices of the Gauss-Seidel method

(equation

(6.19), page 280) and determine the spectral radius of

d) Do

three steps of the Gauss-Seidel method using the original formulation (6.57),

and starting with x(0) = (1, 1, 1), and evaluate the L2

norm of

the difference of two successive approximate solutions.

e) Now

do one partial pivot on the system (6.57) to form the coefficient

matrix

f)

Do three steps of the Gauss-Seidel method using the one-pivot formulation o Exercise

6.2e, and starting with x(0) = (1, 1, 1), and evaluate the L2 norm of the

difference of two successive approximate solutions. g) Do three steps of the

Gauss-Seidel method with successive overrelaxation using the one-pivot formulation

of Exercise 6.2e and wit _ = 0.1, starting with x(0) = (1, 1, 1), and

evaluate the L2 norm of the difference of two successive approximate solutions h)

Do three steps of the conjugate gradient method using the original formulation(6.57),

starting with x(0) = (1, 1, 1), and evaluate the L2 norm of the difference of

two successive approximate solutions

»

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