🧮 Cholesky 分解（2×2）Cholesky Decomposition (2×2)

使用说明与常见问题How-to & FAQ

「Cholesky 分解（2×2）」是什么？What is the Cholesky Decomposition (2×2) tool?

对 SPD 矩阵 [[a,b],[b,c]] 求 L。本地处理。可设置「a」、「b」、「c」。Factor SPD [[a,b],[b,c]] as L Lᵀ. Processed locally. Settings: a, b, c.

如何使用「Cholesky 分解（2×2）」？How do I use the Cholesky Decomposition (2×2) tool?

在「Cholesky 分解（2×2）」中，填写「a」、「b」、「c」等参数，结果会随输入实时计算并显示在下方。In the Cholesky Decomposition (2×2): Fill in "a", "b", "c"; results are recalculated instantly as you type.

能分解更大的矩阵吗？Can it factor a larger matrix?

不能，本页只演示 2×2 对称正定矩阵 [[a, b], [b, c]] = L·Lᵀ，需要 a > 0 且 ac − b² > 0。更大的矩阵按同样的逐列公式计算，可以用数值计算库完成。No, it demonstrates 2×2 only: a symmetric positive-definite [[a, b], [b, c]] = L·Lᵀ, which needs a > 0 and ac − b² > 0. Larger matrices follow the same column-by-column formulas in a numerical library.

能举个计算实例吗？Can you show a worked example?

例如在「Cholesky 分解（2×2）」中填 a = 4，b = 2，c = 3，结果区显示：L₁₁：2；L₂₁：1；L₂₂：1.41421356For example, entering a = 4, b = 2, c = 3 in the Cholesky Decomposition (2×2) gives: L₁₁: 2; L₂₁: 1; L₂₂: 1.41421356

哪些输入会被检查？Which inputs are validated?

「Cholesky 分解（2×2）」会检查这些输入——「a」、「b」、「c」：必须填写；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Cholesky Decomposition (2×2) checks its inputs — "a", "b", "c": required; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.

有哪些选项可以调整？What options can I adjust?

「Cholesky 分解（2×2）」的设置：「a」默认 4；「b」默认 2；「c」默认 3。每次生成结果都按当前设置处理。Settings in the Cholesky Decomposition (2×2) — "a" default 4; "b" default 2; "c" default 3. The result always uses the current settings.

计算精度如何？How precise are the results?

「Cholesky 分解（2×2）」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Cholesky Decomposition (2×2) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.

「Cholesky 分解（2×2）」免费吗？需要注册吗？Is the Cholesky Decomposition (2×2) free? Do I need an account?

「Cholesky 分解（2×2）」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Cholesky Decomposition (2×2) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.