{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chemical Engineering Hand Written_Notes_Part_95

# Chemical Engineering Hand Written_Notes_Part_95 - 192 5...

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

192 5. OPTIMIZATION AND RELATED NUMERICAL SCHEMES Here s i,k are ( i, k ) th elements of sample covariance matrix S ϕ of the random variable vector ϕ . Alternatively, this matrix can also be estimated as S ϕ = Cov ( ϕ ) = 1 N 1 N X j =1 h ϕ ( j ) b ϕ i h ϕ ( j ) b ϕ i T (6.17) = 1 N 1 Φ 1 ³ b ϕ ´ T ¸ T Φ 1 ³ b ϕ ´ T ¸ (6.18) It may be noted that sample covariance matrix S ϕ is an estimated of population covariance matrix Σ . It may be noted that Finally , sample correlation coe cients (normalized or standardized covariances) are de fi ned as r i,k = P N j =1 h φ j,i b ϕ i i h φ j,k b ϕ k i r P N j =1 h φ j,i b ϕ i i 2 r P N j =1 h φ j,k b ϕ k i 2 (6.19) = s i,k s i,i s k,k = s i,k s i s k = £ e ( i ) ¤ T e ( k ) q [ e ( i ) ] T e ( i ) q [ e ( k ) ] T e ( k ) = cos( θ ι,k ) i = 1 , 2 , ...m ; i = 1 , 2 , ...m where s i and s k represents sample standard deviations of ϕ i and ϕ k , respectively, and r i,k represents ( i, k ) th element of sample correlation matrix R ϕ . Here θ ι,k is angle between vectors e ( i

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_95 - 192 5...

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

View Full Document
Ask a homework question - tutors are online