Information:
The Hilbert matrix with entries is notoriously ill-conditioned. For , . A scientific computation uses to model a system where input measurements have 0.01% relative error.
What is the expected relative error in the output?

Question

Information: 
 The Hilbert matrix    with entries    is notoriously ill-conditioned. For   ,   . A scientific computation uses    to model a system where input measurements have 0.01% relative error. 
What is the expected relative error in the output?

Answer

Approximately 2.4% because symmetric matrices use effective    for the error bound

Answer

Approximately 480% because Hilbert entry decay concentrates error in early elimination pivots

Answer

Approximately 0.01% because Hilbert symmetry preserves error magnitudes despite high

Answer

Approximately 48% because the condition number amplifies 0.01% input error by factor 4800

Answer

Approximately 4800% because   , fully unreliable

Answer

Approximately 0.48% because    using square-root amplification

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