Additer — Adaptive Iteration Method

This project visualizes the Adaptive Iteration Method (Additer) for finding the value of a variable where a linear function intersects a given true value.

What the program does

1. Defines a linear function: $y = (1 + \alpha)x + \beta$

2. The goal is to find x such that: $y = \text{True Value}$

3. The program starts from an initial value x0 and adjusts it iteratively to reduce the error. The step size is adaptive:

   • small error → small step
   • large error → large step

4. Each iteration is logged and visualized on a plot.

Plot visualization

The plot shows:

• the line $y = f(x)$
• the line $y = x$
• a horizontal line for the true value
• the steps of the Additer method

This allows visual understanding of how the method converges to the solution.

Main parameters

Constants are defined at the top of the file:

• TRUE_VALUE — the target true value
• ALPHA_PERCENT, BETA_PERCENT — function parameters
• LR_LOW, LR_DEFAULT, LR_HIGH — step sizes
• error thresholds

These parameters can be adjusted as needed.

How the method works

The function additer_alternative():

1. Takes the current x

2. Computes y

3. Computes the error

4. Updates x:

   x_next = x - lr * error

5. Adjusts lr depending on error magnitude

6. Stops if the error is below a threshold

Running the program

Simply run:

python main.py

Output:

• values for each iteration
• final error
• a visual plot of the iterative steps

Use cases

This code can be used for:

• learning adaptive iteration methods
• demonstrating guaranteed convergence
• visualizing root-finding of a linear function