## 4.6-2
##
source('utils.R')

## Solve 4.2-8 to get x^1 using only three significant digits:
##
source('section_4_2_ex_8.R')

## What is the residual r for this approximate solution:
##
residual = W_orig[, 5] - W_orig[, 1:4] %*% x
print('residual= ')
print(residual)

## Solve A e = r (for e)
##
res = GE_w_scaled_partial_pivoting(W_orig[, 1:4], residual)
print('The error vector e=')
print(res$X)

## The new solution using iterative improvement:
##
print(x + res$X)