Question: Do a backward error analysis for the scalar product s = a 1 b 1 + a 2 b 2 + + an bn .

Do a backward error analysis for the scalar product s

=

1

1 +

2

2 + +

an bn

.

Redo the analysis under the assumption that double

-

precision accumulation is used. This means that the double

-

precision results of each multiplication are retained and added to the sum in double precision, with the resulting sum rounded only at the end to single precision.

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