Use the method of Theorem 6.12 (that is, the method we discussed in class) to find a system of equations whose solution would determine the coefficients of the best fit quadratic equation y = ct² + dt + ƒ through the points (0, 1), (2, 2), (3,4), and (4,8). Clearly show your setup including the starting system Ar = y and the resulting system A* Aro = A*y. You need not solve for the coefficients c,d, and ƒ unless you feel strangely compelled to do so. Theorem 6.12. Let A € Mmxn (F) and y € F™. Then there exists ro € F" such that (A*A)ro = A*y and || Aro – y|| < ||Ar – y|| for all z € F". Furthermore, if rank(A) = n, then ro = (A* A)-' A*y.
Use the method of Theorem 6.12 (that is, the method we discussed in class) to find a system of equations whose solution would determine the coefficients of the best fit quadratic equation y = ct² + dt + ƒ through the points (0, 1), (2, 2), (3,4), and (4,8). Clearly show your setup including the starting system Ar = y and the resulting system A* Aro = A*y. You need not solve for the coefficients c,d, and ƒ unless you feel strangely compelled to do so. Theorem 6.12. Let A € Mmxn (F) and y € F™. Then there exists ro € F" such that (A*A)ro = A*y and || Aro – y|| < ||Ar – y|| for all z € F". Furthermore, if rank(A) = n, then ro = (A* A)-' A*y.
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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Transcribed Image Text:Use the method of Theorem 6.12 (that is, the method we discussed in class) to find a system of equations
whose solution would determine the coefficients of the best fit quadratic equation y = ct² + dt + ƒ through the
points (0, 1), (2, 2), (3, 4), and (4,8). Clearly show your sctup including the starting system Ar =y and the
resulting system A* Aro = A*y. You need not solve for the coefficients c, d, and ƒ unless you feel strangely
compelled to do so.
Theorem 6.12. Let A € Mmxn (F) and y e Fm. Then there exists ro E F" such that (A*A)ro = A*y and
|| Aro – y|| < ||Ax – y|| for all r E F". Furthermore, if rank(A) = n, then ro =
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