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##### CSCI 3656 - Colorado Study Resources
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###### Assignment1

Course: Numerical Computation

Assignment 1 CSCI 3656 due January 20, 2011 1. Express the following decimal quantities in binary: 26, 3/8, 91, 39/64. Now express each as rounded normalized machine numbers with base 2 and 4 bits of precision. 2. Consider a hypothetical computer using ba

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###### Assignment12

Course: Numerical Computation

Assignment 12 CSCI 3656 due April 21, 2011 1. (a) On your computer approximate the derivative of the function f (x) = 2.0/(x2 + 3.2) exp(1.2x) at the point x = 1.3 using a two point forward dierence formula. Use as denominators the values h = 2k for k =

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###### Assignment11

Course: Numerical Computation

Assignment 11 CSCI 3656 due April 14, 2011 1. The following set of simulated data gives the quantity of a decaying substance at various times. The substance is composed of three isotopes with decay rates 0.0, 0.8, and 0.9. If the initial quantities are de

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###### Assignment10

Course: Numerical Computation

Assignment 10 CSCI 3656 due April 7, 2011 1. Given data (xi , yi ) for i = 1, . . . , n, in order to compute the cubic spline coecients (bi , ci , di ), you must (i) set up the equations (3.30) on page 175, (ii) solve the tridiagonal system by Gaussian el

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###### Assignment9

Course: Numerical Computation

Assignment 9 CSCI 3656 due March 31, 2011 1. Suppose you constuct a polynomial approximation to the function f (x) = ln(x) on the interval [1,3]. If you use n equally spaced points, give an upper bound for the interpolation error using the error bound for

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###### Assignment8

Course: Numerical Computation

Assignment 8 CSCI 3656 due March 17, 2011 1. For the data (xi , yi ) = (0, 6.0) (1, 4.0) (2, 3.0), (4, 7.0), a) Write down the Lagrange form of the interpolating polynomial p(x). (There is no need to algebraically multiply out the polynomial. Leave it in

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###### Assignment7

Course: Numerical Computation

Assignment 7 CSCI 3656 due March 3, 2011 1. In Matlab the command A=hilb(10) will produce an 10 10 Hilbert matrix, i.e. A(i, j ) = 1/(i+j 1). Compute the right hand side vector b = Av , where v = [1, 2, 3, 4, 5, 1, 2, 3, 4, 5]T . (a) Solve the system Ax =

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###### Assignment6

Course: Numerical Computation

Assignment 6 CSCI 3656 due February 24, 2011 1. (a) By hand use Gaussian elimination with scaled partial pivoting to nd the P, L and U factors of the matrix A: 2 4 1 2 A= 4 4 12 10 ; 6 Verify that P A = LU (b) Now use P, L, and U to solve Ax = b, where 2

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###### Assignment5

Course: Numerical Computation

Assignment 5 CSCI 3656 due February 17, 2011 1. Solve the following system Ax = b by Gaussian elimination with partial pivoting. Use the partial pivoting rule described in class and in Section 2.4.1 of the text. Show all the steps. 4 A= 2 2 2 6 8 3 3 ; b

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###### Assignment4

Course: Numerical Computation

Assignment 4 CSCI 3656 due February 10, 2011 1. Given that the distance in meters fallen from rest by a skydiver is y (t) = ln(cosh(t g k )/k. compute the time taken to fall 85 meters using Newtons method. Here, gravitational acceleration g = 9.8065 m/s/s

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###### Assignment3

Course: Numerical Computation

Assignment 3 CSCI 3656 due February 3, 2011 1. Write a program to nd a root of a given equation f (x) = 0 by the method of bisection. Specications a) It should accept as input two starting points whose function values have opposite signs and a stopping to

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###### Assignment2

Course: Numerical Computation

Assignment 2 CSCI 3656 due January 27, 2011 1. Find a more accurate way to calculate each of the following quantities. a) (x + a)3 a3 ; x close to 0, a near 1. b) (x y ) 1/(x + 2y ) when x > y > 0 1/ c) 1 + 6h 1; h near 0. 2. The quantity Q may be compute

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