ForHosting KIT · Developer Utilities

Fixed-point iteration single-step calculator

Fixed-point iteration is the elementary numerical scheme that seeks a number L equal to g(L) by repeatedly applying an iteration function: start from a guess x_0 and set each next value to g of the previous one.

● BetaFree · in your browser

Run — free How it works & API

Use it from WebAPIEmailTelegramApp soon

Students, tutors, and automation scripts often need exactly one step of that map — not a full convergence loop — so they can check a homework line, compare a hand calculation, or drive an external stopping rule that inspects |x_{n+1} − x_n|. This fixed-point iteration single-step calculator accepts the current estimate x_n and the coefficients of a univariate polynomial g (highest degree first), evaluates x_next equals g of x_n with a stable Horner scheme, and returns the next estimate together with the signed delta and absolute progress. The same pure parse logic powers the free browser widget and the API path, so classroom checks and production pipelines never disagree on a single arithmetic step.

How to use it

Enter your values in the form above. The tool checks them before calculating and shows the result on the same page.

Check your inputs

Use the labels and units shown next to each field. If something is missing or outside the allowed range, the page points to the field to fix.

Use it again or automate it

Use the browser tool for individual checks and the API when you need the same capability in an automated workflow.

What you can do with it

Get an answer now

Enter one set of values and see the result without building a spreadsheet or script.

Compare scenarios

Change one value at a time and rerun the calculation to understand what affects the result.

Automate repeated work

Use the API when the same calculation needs to run inside your product or workflow.

FAQ

How do I use this capability?

Complete the fields above and run it on this page. The form highlights anything that needs attention.

For developers — API access

Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.

API endpoint

POSThttps://api.kit.forhosting.com/calculus/fixed-point-single-step

Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.

Call it from your stack

curl -X POST https://api.kit.forhosting.com/calculus/fixed-point-single-step \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"x_n":0,"coefficients":[0.5,1]}'

const res = await fetch("https://api.kit.forhosting.com/calculus/fixed-point-single-step", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "x_n": 0,
    "coefficients": [
      0.5,
      1
    ]
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/calculus/fixed-point-single-step",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "x_n": 0,
    "coefficients": [
        0.5,
        1
    ]
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/calculus/fixed-point-single-step", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"x_n":0,"coefficients":[0.5,1]}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"x_n":0,"coefficients":[0.5,1]}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/calculus/fixed-point-single-step", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)

Example request

{
  "x_n": 0,
  "coefficients": [
    0.5,
    1
  ]
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "calculus.fixed_point_single_step",
  "status": "queued",
  "_links": {
    "result": "/tasks/tsk_…/result"
  }
}

The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.

Pricing

Per request$0.002

Published price — no tokens, no invented credits. A failed task is never charged.

Errors

HTTP	Code	Meaning
`401`	`unauthorized`	Missing or invalid API key.
`402`	`insufficient_balance`	Your balance doesn't cover the task price.
`404`	`unknown_type`	That task type doesn't exist.
`429`	`rate_limited`	Too many requests. Use the webhook instead of polling.

Read the full KIT documentation →