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ProgrEx3 - Department of Mathematics University of Houston...

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Department of Mathematics University of Houston Numerical Analysis I Dr. Ronald H.W. Hoppe Numerical Analysis I (3rd Practical Homework Assignment) Practical Exercise 3 ( Linear Least Squares Problem ) Write a code which implements the linear least squares problem associated with polynomial approximation (cf. Exercise 18, 5th Homework Assignment) for m = 2 k , k ∈ { K 1 , ..., K 2 } , and n = 2 K 1 . The input data are the parameters K 1 , K 2 and the function f . The output data are the solution vectors x ( m ) with m as above. The doubling of m means the incorporation of m additional conditions. These additional conditions should be added sequentially by using the technique of updating as described in Exercise 19 of the 5th Homework Assignment. The delivery is a table containing the output data for K 1 = 3 , K 2 = 20 and f ( x ) = x . For your control: m solution vector x ( m ) 8 0.0000 4.8527 -24.3118 82.8453 -165.5651 189.7227 -115.3446 28.8009 16 0.0019 5.4852 -33.1230 128.0295 -278.9052 339.2547 -215.0103 55.2682 32 0.0123 5.4496 -34.1508 136.3590 -304.4484 377.4443 -242.8991 63.2366 64 0.0294 4.9875 -29.9577 118.5297 -264.3041 328.1853 -211.7980
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