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Exercise 10: An illustration of the use of a netlib routine, the modification, and the consideration of the errors.

Retrieve the LAPACK routine sgeevx from netlib (see section 11 below on how to do this). Write a modified version, which we will call sgesvn, which does not do pivoting. Run both routines on randomly generated test matrices, and compare the error bounds they compute. Modify the test matrices to make the (1,1) entry very small. How do the error bounds compare now? Note that LAPACK produces other error bounds besides the one described here.