The shift operator E is defined as E[f(xi)] = f(xi + h) and E'[f(xi)] = f(xi -…
2009
The shift operator E is defined as E[f(xi)] = f(xi + h) and E'[f(xi)] = f(xi - h) then △ (forward difference) in terms of E is
- A.
E-1
- B.
E
- C.
1 - E-1
- D.
1 - E
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Correct answer: A
The forward difference operator Δ is defined as Δf(x_i) = f(x_{i+1}) - f(x_i). The shift operator E is defined as Ef(x_i) = f(x_{i+1}). Using the identity operator I where If(x_i) = f(x_i), we can write Δf(x_i) = Ef(x_i) - If(x_i). Thus, the operator relationship is Δ = E - I, or simply Δ = E - 1.