Matrix division \ for sparse and singular matrices

[zdenek_hurak]

Why does julia systematically fails when doing \ operation?

It appears that the convention adopted by Julia is that the backslash symbol used in x = A\b with a square A matrix really stands exclusively for the inverse of a matrix (computed perhaps using LU decomposition). If A is singular (or detected close to singular), the call of x= A\b fails. In such situations, SVD is your friend: julia> G = svd(A) SVD{Float64, Float64, Matrix{Float64}} U factor: 3×3 Matrix{Float64}: -0.332289 0.850246 0.408248 -0.549449 0.177311 -0.816497 -0.766609 -0.4…

Compare with

julia> x1p = pinv(A1)*B1
2-element Vector{Float64}:
 1.9999999999999993
 1.9999999999999993