# hw2 - Homework 2 Foundations of Computational Math 2 Spring...

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Homework 2 Foundations of Computational Math 2 Spring 2011 Solutions will be posted Wednesday, 1/26/10 Written homework problems are study questions. You need not turn in solutions but you are strongly encouraged to do the problems and read the posted solutions carefully. Problem 2.1 Let p n ( x ) be the unique polynomial that interpolates the data ( x 0 , f 0 ) , . . . , ( x n , f n ) Suppose that we assume the form p n ( x ) = α 0 + α 1 ( x - x 0 ) + · · · + α n ( x - x 0 )( x - x 1 ) · · · ( x - x n 1 ) and let a = α 0 . . . α n y = y 0 . . . y n 2.1.a . Show that the constraints yield a linear system of equations La = y where L is lower triangular. 2.1.b . Show that the linear system yields a recurrence for the α i that is equivalent to one of the standard deFnitions of the divided di±erences and therefore this is the Newton form of p n ( x ). Problem 2.2

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hw2 - Homework 2 Foundations of Computational Math 2 Spring...

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