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PDF-InterpolationandApproximationTheBasicProblem:Approximateacontinuousfun PDF document

KeyTheoremGivendistinctnodesx0x1xnandarbitraryf0f1fnthereisauniquepolynomialpnxofdegreeatmostnthatinterpolatesfxatx0x1xnProofExistenceconstructiveLetPnxa0a1xx0anx

KeyTheoremGivendistinctnodesx0;x1;xnandarbitraryf0;f1;fn thereisauniquepolynomialpn(x)ofdegreeatmostnthatinterpolatesf(x)atx0;x1;xn.Proof:Existence:(constructive)LetPn(x)=a0+a1(xx0)+an(x

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