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A hyperbola (curve #1) and an ellipse (curve #2) are respectively described by 1 fi(x, y) = xy -- = 0 2 2 fz(x,») = (k) + (})_i In order to find the intersection points of these two curves, a nonlinear system of equations can be formed and then solved using the Newton-Raphson method. Assuming an initial estimate (guess) -1=0 Yo

A hyperbola (curve #1) and an ellipse (curve #2) are respectively described by 1 fi(x, y) = xy -- = 0 2 2 fz(x,») = (k) + (})_i In order to find the intersection points of these two curves, a nonlinear system of equations can be formed and then solved using the Newton-Raphson method. Assuming an initial estimate (guess) -1=0 Yo

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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Please provide answers to three sig. digits and do not approximate numbers in intermediate steps
(a) Determine the Jacobian matrix J (x, y) F Note: Use the fractional format for numbers and small letters "x" and "y" to express your answers, e.g. 1/2*x^2 for 1x². (b) The estimate of the intersection point after one iteration: x1 0:18 The approximate relative error is (c) The estimate of the intersection point after 3 iterations: 1:48) CH The approximate relative error is (d) After 3 iterations, is it converged if the tolerance is 0.25? No answer is given
Transcribed Image Text:(a) Determine the Jacobian matrix J (x, y) F Note: Use the fractional format for numbers and small letters "x" and "y" to express your answers, e.g. 1/2*x^2 for 1x². (b) The estimate of the intersection point after one iteration: x1 0:18 The approximate relative error is (c) The estimate of the intersection point after 3 iterations: 1:48) CH The approximate relative error is (d) After 3 iterations, is it converged if the tolerance is 0.25? No answer is given
A hyperbola (curve #1) and an ellipse (curve #2) are respectively described by 1 fi(x, y) = xy J2(x,») = (k) + In order to find the intersection points of these two curves, a nonlinear system of equations can be formed and then solved using the Newton-Raphson method. Assuming an initial estimate (guess) XO Yo = = 0 2 2 (²)² + (-)²- - ₁ -1=0 (a) Determine the Jacobian matrix J(x, y) Note: Use the fractional format for numbers and small letters "x" and "y" to express your answers, e.g. 1/2*x^2 for 1x².
Transcribed Image Text:A hyperbola (curve #1) and an ellipse (curve #2) are respectively described by 1 fi(x, y) = xy J2(x,») = (k) + In order to find the intersection points of these two curves, a nonlinear system of equations can be formed and then solved using the Newton-Raphson method. Assuming an initial estimate (guess) XO Yo = = 0 2 2 (²)² + (-)²- - ₁ -1=0 (a) Determine the Jacobian matrix J(x, y) Note: Use the fractional format for numbers and small letters "x" and "y" to express your answers, e.g. 1/2*x^2 for 1x².
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