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A2yo A3yo absolute error accuracy Allied Tables AN/N approximate Central differences Clear input cubic curve cycle register decimal places desk calculating machines differentiation direct interpolation divisor dy/dx Equate coefficients evaluate Everett's formula Example final rounding following table forward difference Given the table giving Hence higher differences Input Operation Cycle integration Interpolation and Allied interpolation formula inverse interpolation Lagrange interpolation formula leading diagonal least significant digit least squares linear interpolation linear simultaneous equations lines from end machine operations mathematical tables method multiply Newton's Numerical Analysis numerical values obtain Operation Cycle Accumulator polynomial quadratic division quadratic factor quotient relative error result round-off errors rounding errors sequence of machine significant figures Simpson's rule square root Step subtraction successive substitution tabular values tabulated function technique third differences transmitted error variable yields