WOLFRAM SYSTEM MODELER
This information is part of the Modelica Standard Library maintained by the Modelica Association.
tk = Matrices.Utilities.findLocal_tk(Rk, Vk);
findLocal_tk() is an auxiliary function called in iterative solver for algebraic Riccati equation based on Newton's method with
exact line search like continuousRiccatiIterative
The function computes the local minimum of the function f_k(t_k)
f_k(t_k) = alpha_k*(1-t_k)^2 + 2*beta_k*(1-t)*t^2 + gamma_k*t^4
by calculating the zeros of the derivation d f_k/d t_k. It is known that the function f_k(t_k) has a local minimum at some value t_k_min in [0, 2].
With t_k_min the norm of the next residual of the algorithm will be minimized.
See  for more information
 Benner, P., Byers, R. An Exact Line Search Method for Solving Generalized Continuous-Time Algebraic Riccati Equations IEEE Transactions On Automatic Control, Vol. 43, No. 1, pp. 101-107, 1998.
Type: Real[:,size(Rk, 1)]
Type: Real[size(Rk, 1),size(Rk, 2)]