23. Consider the problem of finding the vector x of minimum norm satisfying (x|y) 2 6. -1, 2,...," where the y's are linearly independent. (a) Show that this problem has a unique solution. (b) Show that a necessary and sufficient condition that be the solution is that the vector a with components a, satisfy G'a 2e a20 and that a, - 0 if (x)y) > e. Gis the Gram matrix of (y, Y2,..., y).
23. Consider the problem of finding the vector x of minimum norm satisfying (x|y) 2 6. -1, 2,...," where the y's are linearly independent. (a) Show that this problem has a unique solution. (b) Show that a necessary and sufficient condition that be the solution is that the vector a with components a, satisfy G'a 2e a20 and that a, - 0 if (x)y) > e. Gis the Gram matrix of (y, Y2,..., 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:23. Consider the problem of finding the vector x of minimum norm
satisfying
(x|y) 2 6. i-1, 2,...,"
i- 1, 2,.
where the y's are linearly independent.
(a) Show that this problem has a unique solution.
(b) Show that a necessary and sufficient condition that
be the solution is that the vector a with components a, satisfy
G'a 2e
a20
and that a, - 0 if (x)y) >e,. Gis the Gram matrix of (y, Y2,..., y).
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