New formulation for updating parameters


If I want to uses Params = Params + inverse(J'*J + mu * I) * g instead of Params = Params + mu * g,
where J is a Jacobian matrix and J' is transpose of J, and J(i,j) = d loss(i) / d params(j),
and g is a gradient vector, g = J' * loss
and I is identity matrix,
and mu is a scaler.

How can I compute jacobian matrix and inverse(J'*J + mu * I) , and finally update parameters with the above formulation?