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We try to fit a circle with center (C1, c2) and radius r in a least-squares sense to n given points (x;, Y;), i = 1, ., n in the (x, y)-plane, wheren > 3. ...) (i) Derive a system of equations for c1, c2 and r. (ii) Use the substitution c = a/2, c2 = B/2 and r2 = y + c{+ c to bring the system from Part (i) into a form Ax = b. State the form of the matrix A and vector b and express the desired variables (c1, c2, r) in terms of the solution x. ii) Comment on why the condition n > 3 is necessary.

We try to fit a circle with center (C1, c2) and radius r in a least-squares sense to n given points (x;, Y;), i = 1, ., n in the (x, y)-plane, wheren > 3. ...) (i) Derive a system of equations for c1, c2 and r. (ii) Use the substitution c = a/2, c2 = B/2 and r2 = y + c{+ c to bring the system from Part (i) into a form Ax = b. State the form of the matrix A and vector b and express the desired variables (c1, c2, r) in terms of the solution x. ii) Comment on why the condition n > 3 is necessary.

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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We try to fit a circle with center (C1, c2) and radius r in a least-squares sense to n given points (x;, Yi), i = 1, ...,n in the (x,y)-plane, where n > 3. 1, ...,n in the (x, y)-plane, where n > 3. (i) Derive a system of equations for c1, c2 and r. (ii) Use the substitution c = a/2, c2 = B/2 and r2 = y+ c +g to bring the system from Part (i) into a form Ax the desired variables (c1, c2, r) in terms of the solution x. = b. State the form of the matrix A and vector b and express (iii) Comment on why the condition n > 3 is necessary.
Transcribed Image Text:We try to fit a circle with center (C1, c2) and radius r in a least-squares sense to n given points (x;, Yi), i = 1, ...,n in the (x,y)-plane, where n > 3. 1, ...,n in the (x, y)-plane, where n > 3. (i) Derive a system of equations for c1, c2 and r. (ii) Use the substitution c = a/2, c2 = B/2 and r2 = y+ c +g to bring the system from Part (i) into a form Ax the desired variables (c1, c2, r) in terms of the solution x. = b. State the form of the matrix A and vector b and express (iii) Comment on why the condition n > 3 is necessary.
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