The SVD-based method uses the pseudoinverse to solve least squares problems:

$ \mathbf{x} = A^{\dagger}\mathbf{b} $

How it works:

Compute SVD: $A = U\Sigma V^T$, then form the pseudoinverse:

$ A^{\dagger} = V\Sigma^{\dagger}U^T $

where $\Sigma^{\dagger}$ inverts nonzero singular values and transposes.

Advantages:

• Handles rank-deficient matrices automatically
• Most numerically stable method
• Provides minimum-norm solution for underdetermined systems
• Reveals condition number and numerical rank