AMATH 341 / CM 271 / CS 371 Assignment 1 Due : Monday January 18, 2010
1. Implement in Matlab two functions function d = det1(A) and function d = det2(A) to compute the determinant of an n n matrix A using two dierent algorithms. The rst algorithm, det1(A
AMATH 341 / CM 271 / CS 371 Assignment 2 Due : Wednesday January 27, 2010
1. The matrix factor L that emerges from Gaussian elimination with partial pivoting is almost always surprisingly well conditioned. The reason for this is not fully understood. (a)
AMATH 341 / CM 271 / CS 371 Assignment 3 Due : Friday February 5, 2010 Instructor: K. D. Papoulia
1. Recall that a Vandermonde matrix is an nn matrix formed from a vector w = (w0 , w1 , w2 , . . . , wn1 ) as follows: n n 2 w0 2 w0 1 w0 w0 1 n w n1 2 w1 w1
AMATH 341 / CM 271 / CS 371 Assignment 4 Due : Monday February 22, 2010 Instructor: K. D. Papoulia
1. (a) Consider the function f (x) = x/ x2 + 1. This function has a unique root at x = 0. Does Newtons method converge to the root? Implement it in Matlab,
AMATH 341 / CM 271 / CS 371 Assignment 5 Due : Wednesday March 10, 2010 Instructor: K. D. Papoulia
1. In this question you will prove the convergence order for Newtons method. Let x be the root of f (x) = 0 and xk be the k th approximation of this root by
AMATH 341 / CM 271 / CS 371 Assignment 6 Due : Friday March 19, 2010 Instructor: K. D. Papoulia
1. Suppose A is an n n symmetric positive denite matrix. (a) Derive the Cholesky algorithm for factorizing A = RT R, where R is an upper triangular matrix with
AMATH 341 / CM 271 / CS 371 Assignment 7 Due : Monday March 29, 2010 Instructor: K. D. Papoulia
1. Consider a general quadrature scheme for the interval [a, b] that uses distinct quadrature points x1 , . . . , xn and weights w1 , . . . , wn where the weig
AMATH 341 / CM 271 / CS 371 Assignment 8 Due : Monday April 5, 2010 Instructor: K. D. Papoulia
1. Moler exercise 8.7. The El Nino dataset is available on Molers NCM website. 2. Develop an alternative version of the FFT that uses recursion based on powers