Question: Numerical Methods Let A R mn , x R n and y = Ax. Assume x is representable in IEEE oating point arithmetic. Furthermore, let

Numerical Methods

Let A R^mn, x Rⁿ and y = Ax. Assume x is representable in IEEE oating point arithmetic. Furthermore, let y^{^ (hat)} represent the matrix vector product Ax computed in IEEE oating point arithmetic. Perform a backward error analysis to deduce an upper bound on the relative error.

||y^{^}-y||₂/||y||

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