message: Improve documentation of IR
diff: @@ -56,14 +56,14 @@ namespace solver {
  *
  * For any approximation of the solution `solution` to the system `Ax = b`, the
  * residual is defined as: `residual = b - A solution`. The error in
  - * `solution`, `e = x - solution` can be obtained as the solution to the
  - * system `Ae = residual`, since `A e = Ax - A solution = b - A solution =
  - * residual`. Then the real solution is obtained as `x = solution + e`. Instead
  - * of accurately solving the system `Ae = residual`, the solution of the system
  - * `e` can be approximated to obtain the approximation `error` using a coarse
  - * method `solver`, which is used to update `solution`, and the entire process
  - * is repeated with the updated `solution`. This yields the iterative refinement
  - * method:
  + * `solution`, `e = x - solution` (with `x` being the exact solution) can be
  + * obtained as the solution to the residual equation `Ae = residual`, since `A e
  + * = Ax - A solution = b - A solution = residual`. Then, the real solution is
  + * computed as `x = solution + e`. Instead of accurately solving the residual
  + * equation `Ae = residual`, the solution of the system `e` can be approximated
  + * to obtain the approximation `error` using a coarse method `solver`, which is
  + * used to update `solution`, and the entire process is repeated with the
  + * updated `solution`. This yields the iterative refinement method:
  *
  * ```
  * solution = initial_guess
  @@ -80,12 +80,13 @@ namespace solver {
  * residual = inv(A)b - inv(A) A solution = x - solution` it follows that | x -
  * solution* | <= c | x - solution |.
  *
  - * Unless specified otherwise via the `solver` factory parameter, this
  + * Unless otherwise specified via the `solver` factory parameter, this
  * implementation uses the identity operator (i.e. the solver that approximates
  * the solution of a system Ax = b by setting x := b) as the default inner
  - * solver. Such setting results in a relaxation method known as the Richardson
  + * solver. Such a setting results in a relaxation method known as the Richardson
  * iteration with parameter 1, which is guaranteed to converge for matrices
  - * whose spectrum is strictly contained within the unit disc around 1.
  + * whose spectrum is strictly contained within the unit disc around 1 (i.e., all
  + * its eigenvalues `lambda` have to satisfy the equation `|lambda - 1| < 1).
  *
  * @tparam ValueType precision of matrix elements
  */
  