{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chemical Engineering Hand Written_Notes_Part_99

# Chemical Engineering Hand Written_Notes_Part_99 - 200...

This preview shows pages 1–2. Sign up to view the full content.

200 5. OPTIMIZATION AND RELATED NUMERICAL SCHEMES where (7.7) H = 11 / 21 / 3 ... ... 1 /m 1 / / 31 / 4 ... ... 1 / ( m +1) ... ... ... ... ... ... 1 /m ... ... ... ... 1 / (2 m 1) The matrix H is known as Hilbert matrix and this matrix is highly ill-conditioned for m> 3 . The following table shows condition numbers for a few values of m. (7.8) m 3 4 5 6 7 8 c ( H ) 524 1.55e4 4.67e5 1.5e7 4.75e8 1.53e10 Thus, for polynomial models of small order, say m =3 we obtain good sit- uation, but beyond this order, what ever be the method of solution, we get approximations of less and less accuracy. This implies that approximating a continuous function by polynomial of type (7.1) with the choice of basis vectors as (7.3) is extremely ill-conditioned problem from the viewpoint of numerical computations. Also, note that if we want to increase the degree of polynomial to say ( m +1 )from m , then we have to recompute θ 1 , .... , θ m along with θ m +1 . On the other hand, consider the model (7.9) b y ( z )= α 1 p 1 ( z )+ α 2 p 2 ( z α 3 p 3 ( z ............. + α m p m ( z ) where p i ( z )

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

Chemical Engineering Hand Written_Notes_Part_99 - 200...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online