Week05

plot

Cramer's rule

Naive Gauss

do k = 1, n - 1
    do i = k + 1, n
        factor = a(i, k) / a(k, k)
        do j = k + 1, n
            a(i, j) = a(i, j) - factor * a(k, j)
        enddo
        b(i) = b(i) - factor * b(k)
    enddo
enddo

• ill-conditioned systems
• small change in coefficients results in large scale.
• wide range of the answers.

• determinant close to zero.

• condition number

• standardlize -> pick up the maximum element.

• Improve

• use more significant figures
• pick up the great pivot
  • avoid divide zero and round-off error
• scaling
  • we not include scaling into the system.

Flops

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Last update: 2024-04-27