Shanks Transformation Calculator
Free online shanks transformation calculator. Enter your values and get instant results with the formula, step-by-step working, a worked example and FAQs — everything runs locally in your browser on Calcton, no signup required.
中文版：Shanks 变换计算器
原理：Shanks 变换假设部分和 Sₙ = S + A·qⁿ（单指数误差模型），用相邻三项解出 S；对残差反复做同样消除即得迭代 Shanks 表——一级 Shanks 恰是 Aitken Δ² 变换。
步骤：① 选序列；② 输入深度 d；③ 读表末首元素作为最优估计。
示例：几何部分和 Σ1/2^(k-1) 一级 Shanks 即精确得 2；Σ1/k² 十六项部分和误差约 0.04，四级 Shanks 后误差缩小一个数量级以上。
注意事项：Shanks 对单指数误差序列威力最大，对调和型（代数）误差收敛序列效果一般；深度超过项数三分之一时表中元素不足自动停止；表内出现 NaN 说明序列已收敛到机器精度。
相关：Aitken Δ² 计算器是深度 1 的特例；欧拉变换对交错级数提供另一种系统加速路径；Richardson 外推在数值微分中扮演类似角色。
How to use the Shanks Transformation Calculator
- Fill in the inputs with your own numbers — every field shows what it expects.
- The result updates instantly as you type; no "Calculate" click needed.
- Read the result card for the main figure, the step-by-step formula, and practical notes.
Frequently asked questions
Is the Shanks Transformation Calculator free?
Yes — all math calculators on Calcton are free, with no sign-up required. Your inputs are processed in your browser and never sent to a server.
Is there a Chinese version of this tool?
Yes. Use the Chinese version link above — it is the same calculator with the interface in Simplified Chinese.
References
Formulas and benchmarks used by this calculator follow these published sources.
KevinContent LeadCalcton Editorial Team · Last updated 2026-10-04
Kevin maintains Calcton's formula verification and content: every calculator cites the standard it implements, worked examples are recomputed programmatically, and health benchmarks follow WHO and international guidelines.
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