Homework 10

# Homework 10 - Homework Key to,Answer MATH 3315 CSE3365...

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Homework to,Answer Key MATH 3315 I CSE 3365 - F,rtt Semester 2007 Problem 4.2,3: (2 marks) As giverr by @.2) in the lecture notes, the following is the polyrromial interpola- tion error bound for the polynomiai py(r) of degree l/ which interpolates l/ + 1 data {@0, il}Lo ({"0}[o in [o, b]) generated by the function /(r). m.a+,l/(r) -pr',(t)l a max'e,tgtbl l"r-ry+i(r)l -.o{. l"frNt t'(r)1, ;e [o.t] '" (lV + I.)! zefa.bl l" 'l where urr;+r(r) : (n * ,d@ * rr)'. . (t * rN). Now we apply the above inequality to the special case in which pN(r): p1(z) for .1y' : 1 and the 2(: N * 1) data are (rs, fo) : (o,/(a)) and (rr, ft): (b, /(b)), So we have max. l/(rr) - pr(z)l S rela,bl max.r€[o,b] laz@)l -* | f(2)(ztl . z€[a,b] l" 'l' where w2(n) - (r - rs)(r * rr) : (r - a)(r - b). Sir,c" 33ledifl139)l ) 0 and maxze [a,b] lylz) e)l > O, it is obvious that if ==*gf@

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## Homework 10 - Homework Key to,Answer MATH 3315 CSE3365...

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