Smooth Function Academic Question

[semajping]

Dear SuTan:

The smooth function conclusion of Jacobi's solution is given directly in the paper， but I want to know why.

So I did the derivation of smooth function myself, I feel confused.

Assume Loss value E = SIGMA(||P(t) - C(t)||^2 + a * SIGMA(w * ||P(t) - P(r)||^2)
(a means lamda coef)

In order to make value E smaller，I want to take the derivative of E first（Is this true？）
I have 2P(t) - 2C(t) + 2 * a * SIGMA( w * ||P(t) - P(r) ) = 0 , then use Jacobi's solution
but I have an extra 2 before P(t) and C(t), Did I derive it wrong?

I'm going mad, I dreamed about that extra 2 these days

[SuTanTank]

I did the math derivation back in 2015, so it's been a long time and I can't remember the details.
I guess the 2 is just merged into lambda or something, and ignoring it won't affect the result.
The Jacobian iterative solution is just intuitive to me. P(t) should be close to C(t) and P(j), so why not take weighted average of these terms?

[semajping]

Very Thanks