How do I update a table with the aggregated values (min, max) of a related table, fast?

I have a table

create table w (
  id integer primary key,
  --
  min_xyz double,
  max_xyz double,
  min_abc double,
  max_abc double
);

with the min and max values currently being null.

I have another table

create table n (
    id   integer primary key,
    ---
    xyz  float,
    abc  float
);

There is a n:n relation between these tables:

create table n_in_w (
  n_id   integer not null references n,
  w_id   integer not null references w
  --- further attributes
);

Now, I'd like to fill the min and max attributes in w with the respective values in n via the connection via n_in_w. The following would do

update w set 
  min_xyz = (select min(xyz) from n, n_in_w where n.id = n_in_w.n_id and n_in_w.w_id = w.id),
  max_xyz = (select max(xyz) from n, n_in_w where n.id = n_in_w.n_id and n_in_w.w_id = w.id),
  min_abc = (select min(abc) from n, n_in_w where n.id = n_in_w.n_id and n_in_w.w_id = w.id),
  max_abc = (select max(abc) from n, n_in_w where n.id = n_in_w.n_id and n_in_w.w_id = w.id);

but I fear that the performance of this sql query is not optimal as it has to scan n 4 times for each n.id;

Ideally, I am looking for something like

update (
  select
    w.id,
    /*----*/
    w.min_xyz,
    w.max_xyz,
    w.min_abc,
    w.max_abc,
    /*-----*/
    min(n.xyz) min_n_xyz,
    max(n.xyz) max_n_xyz,
    min(n.abc) min_n_abc,
    max(n.abc) max_n_abc
  from 
    w, n_in_w, n
  where
    w.id = n_in_w.w_id and
    n.id = n_in_w.n_id
) i
set
  i.min_xyz = i.min_n_xyz,
  i.max_xyz = i.max_n_xyz,
  i.min_abc = i.min_n_abc,
  i.max_abc = i.max_n_abc;

(or something similar), but it seems it's not possible with mysql.

MySQL syntax:

UPDATE 
      w 
  JOIN
      ( SELECT
              n_in_w.w_id,
              MIN(n.xyz) AS min_n_xyz,
              MAX(n.xyz) AS max_n_xyz,
              MIN(n.abc) AS min_n_abc,
              MAX(n.abc) AS max_n_abc
        FROM 
              n_in_w
          JOIN
              n
            ON 
              n.id = n_in_w.n_id
        GROUP BY
              n_in_w.w_id 
      ) nw
    ON  
      nw.w_id = w.id
SET
      w.min_xyz = nw.min_n_xyz,
      w.max_xyz = nw.max_n_xyz,
      w.min_abc = nw.min_n_abc,
      w.max_abc = nw.max_n_abc;

StackExchange Database Administrators Q#13434, answer score: 8