Tridiagonal Matrix Calculator
Free online tridiagonal matrix 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：三对角方程组求解器
原理：Thomas 算法是高斯消元在三对角阵上的特化——消元只影响相邻两条对角线，前向消去与回代各一遍，乘加次数 8n 左右；样条插值、热传导差分、三对角刚度矩阵都靠它求解。
步骤：① 依次输入次对角、主对角、超对角与右端向量；② 点击求解；③ 查看解与残差。
示例：a = [1, 1]、b = [4, 5, 4]、c = [1, 1]、d = [6, 14, 14] 时解为 [1, 2, 3]，残差为机器精度级；n = 50 时只需约 400 次乘加，通用消元要 125000 次以上。
注意事项：主对角出现零或消元中除数过小会破坏稳定性，严格对角占优时绝对安全；输入长度必须匹配（a 与 c 为 n − 1）；方程组不是三对角结构时本算法不适用，应改用通用求解器。
相关：高斯-赛德尔计算器迭代解一般稀疏阵；三次样条插值工具内部就用三对角求解；条件数计算器评估矩阵的数值稳定性。
How to use the Tridiagonal Matrix 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 Tridiagonal Matrix 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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