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Given the data X 1 0 5 2.5 6.5 3 7 (a) Calculate / (3.4) using Newton's interpolating polynomials of order 1, 2 and 3. [b] Repeat (a) but use the Lagrange polynomial Choose the sequence of the points for your estimates to attain the best possibla 5 1

Given the data X 1 0 5 2.5 6.5 3 7 (a) Calculate / (3.4) using Newton's interpolating polynomials of order 1, 2 and 3. [b] Repeat (a) but use the Lagrange polynomial Choose the sequence of the points for your estimates to attain the best possibla 5 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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D Question 1 Given the data x fibx) 1 0 T, °C 6505228 10 (a) Calculate / (3.4) using Newton's interpolating polynomials of order 1, 2 and 3. (b) Repeat (a) but use the Lagrange polynomial Choose the sequence of the points for your estimates to attain the best possible accuracy. That is, the points should be centered around and as close as possible to the unknown. 15 2 5 Question 2 The table below lists values for dissolved oxygen concentration in water as a function of temperature and chloride concentration. a) Use quadratic and cubic interpolation to determine the oxygen concentration for T 12 °C and c= 10 g/L. b) Repeat (a) but use the Lagrange polynomial 30 Dr. K. Mensah-Darkwa 2.5 6.5 c=0 g/L 14.6 12.8 11.3 10.1 Dissolved Oxygen (mg/L) for Temperature (°C) and Concentration of Chloride (g/L) c = 10 g/L 12.9 11.3 10.1 9.09 8.26 7.56 3 7 CH 9.03 8.17 7.46 6.85 4 hp c = 20 g/L 11.4 10.3 Dissolved oxygen concentration in water as a function of temperature (C) and chloride concentration (g/L). 8.96 8.08 5 1 7.35 6.73 6.20 CHE 358-2015/16
Transcribed Image Text:D Question 1 Given the data x fibx) 1 0 T, °C 6505228 10 (a) Calculate / (3.4) using Newton's interpolating polynomials of order 1, 2 and 3. (b) Repeat (a) but use the Lagrange polynomial Choose the sequence of the points for your estimates to attain the best possible accuracy. That is, the points should be centered around and as close as possible to the unknown. 15 2 5 Question 2 The table below lists values for dissolved oxygen concentration in water as a function of temperature and chloride concentration. a) Use quadratic and cubic interpolation to determine the oxygen concentration for T 12 °C and c= 10 g/L. b) Repeat (a) but use the Lagrange polynomial 30 Dr. K. Mensah-Darkwa 2.5 6.5 c=0 g/L 14.6 12.8 11.3 10.1 Dissolved Oxygen (mg/L) for Temperature (°C) and Concentration of Chloride (g/L) c = 10 g/L 12.9 11.3 10.1 9.09 8.26 7.56 3 7 CH 9.03 8.17 7.46 6.85 4 hp c = 20 g/L 11.4 10.3 Dissolved oxygen concentration in water as a function of temperature (C) and chloride concentration (g/L). 8.96 8.08 5 1 7.35 6.73 6.20 CHE 358-2015/16
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