FLC FLIES AS MUCH AS 800 FT LOW DURING AN ARR INTO LAX.

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ON APCH TO LAX WE WERE SLOWED TO 250 KIAS OR LESS FROM FL410 TO 2100 FT. WE HAD NUMEROUS CHANGES IN ARRS ON THE APCH. THE LAST 4 AIRSPD CHANGES EXCEEDED THE AUTOFLT SYS CAPABILITY. CHANGES FROM 210 KTS TO 190 KTS; TO 210 KTS TO 170 KTS HAD TO BE HAND FLOWN AND ALT RESTRS BUILT INTO FMC NEGATED. AFTER LNDG SOCAL APCH WAS CALLED AND THEY SAID WE WERE 800 FT LOW ON ONE OF THE STAR RESTRS. WE HAD NO ALT WARNINGS ON OUR APCH. IT MAY BE THAT THE FO SET THE ALT ALERT TO INITIAL APCH PRIOR TO THE LAST RESTR. HOWEVER; DUE TO THE INCREASE BACK TO 210 KTS WITHIN 4 MI OF THE MARKER IT WOULD HAVE BEEN IMPOSSIBLE TO LAND WITHOUT GETTING BELOW THE GS OUTSIDE THE OM. AS IT WAS; WE CAME VERY CLOSE TO A MANDATORY GAR DUE TO TOO HIGH A SPD AND DSNDING TOO CLOSE TO THE MARKER. THERE WAS A B737 ON APCH TO ANOTHER PARALLEL RWY WHICH WE CALLED VISUAL TO THE APCH CTL. IT APPEARS THE EXCESSIVE INCREASE IN SPD FROM 190 KTS TO 210 KTS WAS ISSUED OPPOSITE WHAT WAS NEEDED AS THE 210 KTS WAS CHANGED TO 170 KTS AS THE B737 WAS RAPIDLY OVERTAKEN AT 3-4 MI AT 1-2 O'CLOCK. THESE SPD CHANGES REQUIRED FULL SPD BRAKES; FLAP AND GEAR TO COMPLY WITH WHILE DSNDING. BETTER (MORE TIMELY) SPD CHANGES WERE NEEDED.