X1 xí V = 1 X2 X3 det V = (x2 – x1)(x3 – x)(x3 – x2) Let x1, x2 and x3 be fixed numbers all distinct. Matrix V can be used to find an interpolating quadratic polynomial for the points (x1, yı), (x2, y2) and (x3, y3), where y1 , y2 and y3 are arbitrary prove the existence of an interpolating polyno- mial p(t) = co +c¡t + c2t² such that p(x1) = y1, p(x2) = У, and p(x;) — Уз .
X1 xí V = 1 X2 X3 det V = (x2 – x1)(x3 – x)(x3 – x2) Let x1, x2 and x3 be fixed numbers all distinct. Matrix V can be used to find an interpolating quadratic polynomial for the points (x1, yı), (x2, y2) and (x3, y3), where y1 , y2 and y3 are arbitrary prove the existence of an interpolating polyno- mial p(t) = co +c¡t + c2t² such that p(x1) = y1, p(x2) = У, and p(x;) — Уз .
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1
X1
V
1
X2
X3
det V =
(x2 – x1)(x3 – X)(x3 – x2)
Let x1, x2 and x3 be fixed numbers all distinct. Matrix V can
be used to find an interpolating quadratic polynomial for the
points (x1, yı), (x2, y2) and (x3, y3), where y , y2 and y3 are
arbitrary
prove the existence of an interpolating polyno-
mial p(t) = co +c;t + c2t² such that p(x1) = y1, p(x2) =
V2 and p(x3) = y3 ·
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