Broyden-algorithm.md

@@ -4,20 +4,20 @@ Broyden algorithm is implemented according prescription provided in the paper:
 
 `st-wslda` codes support two types of updating schemes of densities:
 * linear mixing, according to formulas (3),
-* Broyden mixing, according to prescription given in sec III.B.
+* Broyden mixing, according to the prescription given in sec III.B.
 
-# Controlling Broyden algorithm
-In order to activate the Broyden mixing user must activate following flag in the *input* file: 
+# Controlling the Broyden algorithm
+In order to activate the Broyden mixing user must activate the following flag in the *input* file: 
  
 ```bash
 broyden                 1        # activate broyden mixing, default=0 (linear mixing)
 ```
-There are two parameters that control mixing parameter (alpha parameter)
+There are two parameters that control the mixing parameter (alpha parameter)
 ```bash
 linearmixing            0.5      # mixing parameter (alpha) for linear mixing, default=0.5
 broydenmixing           0.75     # mixing parameter (alpha) for Broyden mixing, default=0.75
 ```
-We separate these two parameters as in general they may be different. The remaining parameters controlling the Broyden algorithm are:
+We separate these two parameters because, in general, they may differ. The remaining parameters controlling the Broyden algorithm are:
 ```bash
 Mbroyden                5       # number of previous iterations used by Broyden, default=5 
 
@@ -36,15 +36,15 @@ stopbroyden             100     # Broyden is deactivated for iteration it=stopbr
 broydenautores          1       # automatic restarts of Broyden algorithm: 0-no, 1-yes (default)
                                 # the Broyden is automatically restarted if significant changes 
                                 # between two consecutive iterations is detected. 
-broydenEmaxchg          0.1     # if the total energy between iteration change by more than broydenEmaxchg [in Effg units]
+broydenEmaxchg          0.1     # if the total energy between iterations changes by more than broydenEmaxchg [in Effg units]
                                 # then Broyden is restarted, (default=0.1)
 broydenEdelay           5       # scan energy changes only after broydenEdelay with Broyden has been executed 
-                                # typically, just after starting the Broyden energy fluctuations are observed 
+                                # typically, just after starting, the Broyden energy fluctuations are observed 
                                 # which should decay within a few iterations (default=5)
 
 # Recommendation: Use startbroyden and stopbroyden only if Broyden fails to converge. 
-#                 According to experience of our collaborators, there are cases (physical problems)
-#                 where activating Broyden only for some number of iteration provides the best performance 
+#                 According to the experience of our collaborators, there are cases (physical problems)
+#                 where activating Broyden only for some number of iterations provides the best performance 
 
 # For advanced users 
 omega0broyden           0.01    # weight omega_0, see eqn. (6)