# Tag Info

Accepted

### Determinant of large matrices: there's GOTTA be a faster way

No, this is not the way that any (sane) person would compute a determinant. This is not even the way a computer would calculate a determinant! It requires a sum over $n!$ terms, which quickly becomes ...
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### What does QR decomposition have to do with least squares method?

Overview Difficulties in understanding why we use QR-decompositions to find linear least squares could arise either because the mathematics is poorly motivated (why would we choose this method?) or ...
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### What is the most efficient way to find the inverse of large matrix?

Let's solve $Ax = b$. The first equation in this linear system tells us that $-x_0 + a_0 x_n = b_0$, or $$x_0 = a_0 x_n - b_0.$$ The second equation tells us that \begin{align} & x_0 - x_1 + ...
• 52.4k
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• 5,175

### LU Decomposition vs. QR Decomposition for similar problems

I recognize that I'm probably far too late for my answer to be of much use to you, but I'll add an answer here for posterity. First, regarding the choice of method: MATLAB has a very clear ...
• 357
Accepted

### Why is solving linear equation more stable than directly computing matrix inverse?

If $x$ is computed by LU factorization, the residual can be bounded by $$\|b-Ax\|\leq cu\||L||U|\|\|x\|.$$ Assuming for simplicity that $A^{-1}$ is computed exactly and that the only source of error ...
• 23.2k