MATH 307 Lecture Notes - Lecture 7: Interpolation, Vandermonde Matrix
MATH 307 verified notes
7/40View all
Document Summary
I 2 interpolation suppose we have data points xi yi. Xn yn e. g here xi"s can beinputsof system and yi"s are observations or outputs. We want to findan that generates thesedata points. Thisrule canbe understood as a function that passes throughall thesedatapoints explanation eg l. So there mustbe some restrictionson the candidate functions. I 2. 2 langrange interpolation eg i 4 1215 13 l. Pl3 tax 1 a3 ai 12 tar 1as. Al 2 t 2 az 193 5 ai 32 az. 4 a linear equations in the coefficients ai a2 a3. Langrange interpolation given n we canfind a degree in 1 polynomialpix aix tazxn 2 1 with plxi yifor l e i en s of data points x y. 1antxt aixin tazxin 2 t p xi plxu aixin ta xan t pains a xan ta xn t tan ix t an yi. Tan 1 2 tan yz an 1xn tan_in linearequations in coefficients ai ar a3 xn"s are numbers.
