CalcNum-14_2d-C-L1 - 21.08.2014 Primeira lista de exerccios...

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21.08.2014 Primeira lista de exerc´ ıcios — C´ alculo Num´ erico / Turma C Depto. de Matem´ atica – UnB 1 – Sejam as quatro tabelas abaixo: A : x i y i - 3 r - 2 21 - 1 2 0 1 1 0 2 5 B : x i y i - 3 r - 2 21 - 1 2 0 1 1 0 C : x i y i - 3 r - 2 21 - 1 2 0 1 D : x i y i - 3 r - 2 21 - 1 2 0 1 1 0 2 - 19 a) Existe (ao menos) um n´umero r R de tal modo que a tabela A possa ser interpolada por um polinˆ omio de grau no m´ aximo 3? Responda a mesma pergunta para as tabelas B , C e D . b) Em qual(is) dessas tabelas existe um (e somente um) r R para tal interpola¸c˜ ao de grau no m´ aximo 3? Calcule efetivamente tal(is) r (’s). c) Tomando-se r := - 1, fa¸ ca a interpola¸c˜ ao da tabela C pelo sistema linear X~a = ~ y , cuja matriz X ´ e a matriz de Vandermonde definida pelos x i ’s e o vetor cte ~ y ´ e definido pelos y i ’s. d) Tomando-se novamente r := - 1, fa¸ca a interpola¸ ao das tabelas A e D pelos demais 5 etodos: Lagrange, Lagrange igualmente espa¸ cado, Newton/diferen¸ ca dividida e diferen¸ca finita progressiva e regressiva. 2 – Verifique abaixo a tabela com a popula¸ ao mundial (em trilh˜ oes de habitantes) a cada d´ ecada desde 1950 at´ e 2000 (´ultimo dado): ano 1950 1960 1970 1980 1990 2000 popula¸
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