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The Interpolating Polynomial
Numerical Differentiation and Integration
6 other sections not shown
accuracy Adams-Bashforth Adams-Moulton approximate consider correct to 6D cumulative truncation error decimal place degree not greater difference equation estimate the value Euler's method evaluate following theorem formulae 3.4 forward difference formula function Gauss-Seidel method given by Eqn graph Hence hf(xn hypothesis inequality initial value problem integration interpolating points interpolating polynomial interval iterations Jacobi method Lemma Let xk linear systems magnitude matrix Newton's backward difference Newton's forward difference Newton's method numerical analysis Numerical Differentiation numerical solution obtain a bound otherwise go Pn(x polating polynomial polynomial of degree polynomial pn positive integer real number rectangle rule relative error result root rounding error Runge-Kutta methods secant method sequence xn significant figures Simpson's rule solution of Eqn solve starting values tabular values tabulated Taylor expansion method Taylor's algorithm Taylor's theorem Theorem 4.3 trapezium rule truncation and rounding vector whence xn+1 y(xn yn+1