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iii. Is the 3-points forward differon formula appropriate to e Consider the following data: o estimate & UTM r 0.4 0.6 0.8 y1.63 2.22 3.35 4.79 5.05 UT i. Approximate f"(0.8) using 5-points difference formula, ii. Estimate the f (0.4) by using 3-points forward difference formula. UTM UTM UTM UTM iii. Is the 3-points forward difference formula appropriate to estimate f'(1.0). State the reason.

iii. Is the 3-points forward differon formula appropriate to e Consider the following data: o estimate & UTM r 0.4 0.6 0.8 y1.63 2.22 3.35 4.79 5.05 UT i. Approximate f"(0.8) using 5-points difference formula, ii. Estimate the f (0.4) by using 3-points forward difference formula. UTM UTM UTM UTM iii. Is the 3-points forward difference formula appropriate to estimate f'(1.0). State the reason.

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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a) Consider the following data: UTM UTM & UTM x 0.4 UT 0.6 0.8 y 1.63 2.22 3.35 4.79 5.05 1.0 27UTM UTM ii. Estimate the f' (0.4) by using 3-points forward difference formula. SUTM UTM UT UTM UTMUTM f'(1.0). State the reason. UTM b) Consider the matrix d UTM UT UTM UTM 6 UTM UTM UTM 21 AUT A = -1 5 4 i. Compute the dominant eigenvalue, A1 and the corresponding eigen- 5UTM UTM UTM TM &UTM 5 UT vector x1 for the matrix A using power method starting with x = (1,1,1)" and stop the iterations when |m41-m| < 0.05. UTM &UT UTM ii. Determine the smallest eigenvalue, A, for matrix A by using shifted & UTMUTM UTM UTM power method based on the results in (i). Start the iteration UTM UT - X' %3D UTM UTM UTM UTM UT UTM UT
Transcribed Image Text:a) Consider the following data: UTM UTM & UTM x 0.4 UT 0.6 0.8 y 1.63 2.22 3.35 4.79 5.05 1.0 27UTM UTM ii. Estimate the f' (0.4) by using 3-points forward difference formula. SUTM UTM UT UTM UTMUTM f'(1.0). State the reason. UTM b) Consider the matrix d UTM UT UTM UTM 6 UTM UTM UTM 21 AUT A = -1 5 4 i. Compute the dominant eigenvalue, A1 and the corresponding eigen- 5UTM UTM UTM TM &UTM 5 UT vector x1 for the matrix A using power method starting with x = (1,1,1)" and stop the iterations when |m41-m| < 0.05. UTM &UT UTM ii. Determine the smallest eigenvalue, A, for matrix A by using shifted & UTMUTM UTM UTM power method based on the results in (i). Start the iteration UTM UT - X' %3D UTM UTM UTM UTM UT UTM UT
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