Matrix Computation by Golub G.H. and van Loan C.F. 的習題兩題
P.2.1.5 Assume that both A and A+uv^T are nonsingular where A is in
R^(nxn) and u ,v are in R^(n). Show that if x solves (A+uv^T)x=b, then
it also solves a perturbed right hand side problem of the form
Ax = b + αu. Give an expression for αin terms of A, u, and v.
想法：利用 (A + uv^T)^(-1) = A^(-1) - (1+v^T A^(-1) u)^(-1) A^(-1)uv^T A^(-1)
把x先解出來之後代入，但總是整理不出αu，因為有一個b總是消不掉。
P.2.3.10. Suppose A is in R^(mxn) , y is in R^m, and 0≠s is in R^n.
Show that E = ( y-As )s^T / s^T s has the smallest 2-norm of all mxn matrices
that satisfy (A+E)s = y .
沒有什麼想法。
感謝解答！
※ 編輯: iamwjy 來自: 122.117.200.15 (10/01 09:49)