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Show that the Newton divided-difference polynomials 3 - 2(х + 1) +0(х + 1)х + (х + 1)x(х — 1) and -1+4(х+ 2) - 3(х + 2)(х + 1) + (x+2)(х+ 1)х keth interpolate the data (-2, –1), (–1,3), (0, 1), (1, –1), (2, 3). Why do the polynomials not violate the uniqueness property of interpolating polynomials?

Show that the Newton divided-difference polynomials 3 - 2(х + 1) +0(х + 1)х + (х + 1)x(х — 1) and -1+4(х+ 2) - 3(х + 2)(х + 1) + (x+2)(х+ 1)х keth interpolate the data (-2, –1), (–1,3), (0, 1), (1, –1), (2, 3). Why do the polynomials not violate the uniqueness property of interpolating polynomials?

Advanced Engineering Mathematics
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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Show that the Newton divided-difference polynomials 3 — 2(х + 1) +0(х + 1)х + (х + 1)x(х — 1) and —1+ 4(х + 2) - 3(х + 2)(х + 1) + (х+ 2)(х + 1)x both interpolate the data (-2, –1), (–1,3), (0,1), (1, –1), (2,3). Why do the polynomials not violate the uniqueness property of interpolating polynomials?
Transcribed Image Text:Show that the Newton divided-difference polynomials 3 — 2(х + 1) +0(х + 1)х + (х + 1)x(х — 1) and —1+ 4(х + 2) - 3(х + 2)(х + 1) + (х+ 2)(х + 1)x both interpolate the data (-2, –1), (–1,3), (0,1), (1, –1), (2,3). Why do the polynomials not violate the uniqueness property of interpolating polynomials?
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