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Numerical analysis proof

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Recall that a given vector norm |X| the operator norm of matrix A is given by ......

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https://brainmass.com/math/numerical-analysis/numerical-analysis-proof-196347

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This provides an example of a proof regarding a vector norm and a matrix.

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Proof in Numerical Analysis: Taylor's Theorem

Suppose that y(x)' : f(x,y(x)) on the interval [x0, x1] with y (x0) = y0. Assume that a unique solution y exists such that it and all of its derivatives up to and including the third order are defined and continuous on [x0, x1]. Using Taylor's Theorem (and the Mean Value Theorem, if necessary) prove that...

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