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Search results with tag "Taylor s theorem"
Rate of Convergence - Gordon College
math-cs.gordon.eduwhy Newton’s method converges so quickly (when it converges at all). Theorem 2. Let r be a xed-point of the iteration x n+1 = g(x n) and suppose that g0(r) = 0 but g00(r) 6= 0 . Then the iteration will have a quadratic rate of convergence. Proof. Using Taylor’s Theorem once again, but including one more term, we have g(x) = g(r) + g0(r)(x r ...
The Integral Form of the Remainder in Taylor’s Theorem ...
www.math.umd.eduThe Integral Form of the Remainder in Taylor’s Theorem MATH 141H Jonathan Rosenberg April 24, 2006 Let f be a smooth function near x = 0. For x close to 0, we can write f(x) in terms of