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Minimizing the length of the residual vector r = b – Ax is equivalent of mini- mizing the quadratic form Q(x) = r"r = (b – Ax)"(b – Ax) = b"b – 2x"A™b+x"ATAx. Recall yourself how to calculate the derivative of a vector-valued function F(x) with respect to a vector x. Try to find out the expression of x by differentiating the equation above.

Minimizing the length of the residual vector r = b – Ax is equivalent of mini- mizing the quadratic form Q(x) = r"r = (b – Ax)"(b – Ax) = b"b – 2x"A™b+x"ATAx. Recall yourself how to calculate the derivative of a vector-valued function F(x) with respect to a vector x. Try to find out the expression of x by differentiating the equation above.

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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Problem 3 Minimizing the length of the residual vector r = b – Ax is equivalent of mini- mizing the quadratic form Q(x) = r'r = (b – Ax)" (b – Ax) = b"b – 2x"A'b+x"A"Ax. Recall yourself how to calculate the derivative of a vector-valued function F(x) with respect to a vector x. Try to find out the expression of x by differentiating the equation above.
Transcribed Image Text:Problem 3 Minimizing the length of the residual vector r = b – Ax is equivalent of mini- mizing the quadratic form Q(x) = r'r = (b – Ax)" (b – Ax) = b"b – 2x"A'b+x"A"Ax. Recall yourself how to calculate the derivative of a vector-valued function F(x) with respect to a vector x. Try to find out the expression of x by differentiating the equation above.
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