Reference for direct interpolation used

[mohdibntarek]

What is the reference for the direct interpolation used in this package? I see that it is an extension to non Z matrices but is there a paper or book that describes the rationale?

[learning-chip]

I found it in Trottenberg's Multigrid book -> Appendix A. An Introduction to Algebraic Multigrid (by Klaus Stuben) -> Section A.4.2 Direct Interpolation -> A.4.2.3 General case (compared to the more commonly-seen formula in Section A.4.2.1 M-matrices)

[termi-official]

Sorry to bother, but I think the reference does not match the actual implementation. One of my students found this. I fail to understand the discrepancy, too. In these lines here

AlgebraicMultigrid.jl/src/classical.jl

Lines 158 to 162 in 7bb7e05

	if sval < 0
	Bx[nnz] = abs(neg_coeff * sval)
	else
	Bx[nnz] = abs(pos_coeff * sval)
	end

Here an abs pops up (introduced in #43), while the original general formula given by Klaus Stuben's An Introduction to Algebraic Multigrid (A.4.2.3 - Equation 83f) states that the weights are signed, i.e.

$$w_{ik} = \begin{cases} - \alpha_i a_{ik} / a_{ii} & \text{if } k\in P_i^- \\\ - \beta_i a_{ik} / a_{ii} & \text{if } k\in P_i^+ \\\ \end{cases}$$

such that $w_{ik} < 0$ for $k\in P_i^-$ and $w_{ik} > 0$ for $k\in P_i^+$.

Can someone help me here what I got wrong?