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A₁ A₂ B₁ C₁ centered form Chapter contain zero convergence corresponding decimal defined degenerate intervals derivatives differential system Digital Computation elements ERROR BOUND Error in Digital evaluation exact result exact solution example finite number follows formulas function f given initial values initial-value problem integral equation interval arith interval arithmetic interval arithmetic operations interval extensions interval matrix interval numbers interval of values interval solution interval vector intervals containing Lemma lower bounds machine arithmetic machine-computed metic metric space obtain ordinary differential equations pair procedure range of values rational expression rational interval function real arithmetic real numbers real rational function real restriction real variable real-valued round-off error rounded-interval arithmetic S₁ satisfies Section SHARE program single-precision solution y(x subintervals subroutines suppose Taylor coefficients Taylor expansions Taylor series Theorem 3.1 tion united extension values of ƒ w(X₁ width X₁ y₁ y₁(x Y₂ zero of ƒ