CSC_349_HANDOUT#24

# CSC_349_HANDOUT#24 - COMPUTER SCIENCE 349A Handout Number...

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

1 COMPUTER SCIENCE 349A Handout Number 24 CUBIC SPLINE INTERPOLANTS The following definition is the same as given in points 1-5 on pages 501-502 of the 5 th ed. (pages 515-516 of the 6 th ed.), but is more precise. Definition Given data < + , ) ( , ), ( ), ( and , with , , , 1 0 1 1 0 n i i n x f x f x f x x x x x K K S ( x ) is a cubic spline interpolant for ) ( x f if (a) S ( x ) is a cubic polynomial, denoted by S j ( x ) , on each subinterval 1 0 , ] , [ 1 + n j x x j j (b) ) ( ) ( j j j x f x S = , for 1 0 n j and ) ( ) ( 1 n n n x f x S = (c) ) ( ) ( 1 1 1 + + + = j j j j x S x S , for 2 0 n j (d) ) ( ) ( 1 1 1 + + + = j j j j x S x S , for 2 0 n j (e) ) ( ) ( 1 1 1 + + + = j j j j x S x S , for 2 0 n j and (f ) either one of the following hold: (i) S ( x 0 ) =′ S ( x n ) = 0 --- the free or natural boundary conditions or (ii) ) ( ) ( 0 0 x f x S = and ) ( ) ( n n x f x S = ---

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

CSC_349_HANDOUT#24 - COMPUTER SCIENCE 349A Handout Number...

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

View Full Document
Ask a homework question - tutors are online