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Rounding errors 1 0 + 1 0 p t Computers use finite precision to represent real numbers, which leads to rounding. You can see the
Rounding errors Computers use finite precision to represent real numbers, which
leads to rounding. You can see the size of the rounding error for real numbers around using the
MATLAB command eps or the numpy command npspacing This number, also called
the machine epsilon, is dots for the standard double precision representation of
numbers in a computer. Try the following experiments in MATLAB or PythonOctaveJulia
a The th Hilbert matrix has the entries for dots,
It is known that solving systems with the Hilbert matrix increases rounding errors since the
matrix is poorly conditioned. Let be the column vector of length that contains all s
Report the exact and the numerically computed values for
for
Here, is the norm. Also report the norm, norm and norm condition numbers
of for
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