Numerical Patterns

Convergence Steps

Halve an Error

Many numerical methods repeatedly reduce an error estimate. A small bounded loop can show the shape without doing heavy computation.

Program

Play the program to choose how many halving steps are applied.

convergence_steps.f90 
program convergence_steps_demo
    implicit none
    integer :: step_count
    integer :: i
    real :: error

    step_count = 
    error = 1.0
    do i = 1, step_count
        error = error / 2.0
    end do
    print '(F0.3)', error
end program convergence_steps_demo

program convergence_steps_demo
    implicit none
    integer :: step_count
    integer :: i
    real :: error

    step_count = 
    error = 1.0
    do i = 1, step_count
        error = error / 2.0
    end do
    print '(F0.3)', error
end program convergence_steps_demo

program convergence_steps_demo
    implicit none
    integer :: step_count
    integer :: i
    real :: error

    step_count = 
    error = 1.0
    do i = 1, step_count
        error = error / 2.0
    end do
    print '(F0.3)', error
end program convergence_steps_demo
bounded loop `do i = 1, step_count` keeps the iteration count explicit.
error update Each loop halves the current error estimate.
convergence Repeated reduction shows the approach toward zero without relying on timing.