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15. Find a polynomial P(x) of degree < 3 for which P(1) = y2 P'(1) = y2 P(0) = y1, P'(0) = y, with y1, y2, y, y given constants. The resulting polynomial is called the cubic Hermite interpolating polynomial. Hint: Write P(x) = yı H1 (x) + y{ H2(x) + y2 H3 (x)+ y½H4(x) with H1, H2, H3, H4 cubic polynomials satisfying appropriate properties, in anal- ogy with (4.15). For example, choose H1(x) to be a cubic polynomial that satisfies H (0) = 1, Н (1) — 0 H{(0). = 0, H{(1) =

15. Find a polynomial P(x) of degree < 3 for which P(1) = y2 P'(1) = y2 P(0) = y1, P'(0) = y, with y1, y2, y, y given constants. The resulting polynomial is called the cubic Hermite interpolating polynomial. Hint: Write P(x) = yı H1 (x) + y{ H2(x) + y2 H3 (x)+ y½H4(x) with H1, H2, H3, H4 cubic polynomials satisfying appropriate properties, in anal- ogy with (4.15). For example, choose H1(x) to be a cubic polynomial that satisfies H (0) = 1, Н (1) — 0 H{(0). = 0, H{(1) =

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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15. Find a polynomial P(x) of degree < 3 for which P(0) = y1, P'(0) = y, P(1) = y2 P'(1) = y2 with y1, y2, y1, y½ given constants. The resulting polynomial is called the cubic Hermite interpolating polynomial. Hint: Write P(x) = yı H1 (x) + y{ H2(x) + Y2H3 (x)+ y½H4(x) with H1, H2, H3, H4 cubic polynomials satisfying appropriate properties, in anal- ogy with (4.15). For example, choose H1 (x) to be a cubic polynomial that satisfies H1(1) = 0 H{(1) = 0 H1 (0) = 1, %3D H{(0). = 0,
Transcribed Image Text:15. Find a polynomial P(x) of degree < 3 for which P(0) = y1, P'(0) = y, P(1) = y2 P'(1) = y2 with y1, y2, y1, y½ given constants. The resulting polynomial is called the cubic Hermite interpolating polynomial. Hint: Write P(x) = yı H1 (x) + y{ H2(x) + Y2H3 (x)+ y½H4(x) with H1, H2, H3, H4 cubic polynomials satisfying appropriate properties, in anal- ogy with (4.15). For example, choose H1 (x) to be a cubic polynomial that satisfies H1(1) = 0 H{(1) = 0 H1 (0) = 1, %3D H{(0). = 0,
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