Variational Analysis of Some Conjugate Gradient Methods
Variational Analysis of Some Conjugate Gradient Methods
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In our eReader you can find the full English version of the book. Read Variational Analysis of Some Conjugate Gradient Methods Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Variational Analysis of Some Conjugate Gradient Methods
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We first describe the method developed by Concus, Golub [5] and Widlund [46], which is commonly known as the CGW method. The Galerkin condition has the form (32) and, as in the symmetric, positive definite case, it is satisfied by x k — x = Vky k, where y 9 k is the solution of (68) V k T AV k yi = V k T r .
From (24), (28) and (67), it follows that (68) is equivalent to (69) Rk(I-Jk)y 9 k = Pie W .
We note that p t = (uj, Mv{) is the first element of the diagonal matrix R k and that we therefo...re can simplify equation (69) to (70) (I-J k )y 9 k = e (1) .
With the normalization given by (20), the LU factorization of (/ — J k ) = L k Uk requires no arithmetic; this is the reason for chosing (3 k in this way. The factors are i i r& i -i i i i -i i u k -72 03 -73 A >*+i 18 It is also easy to see that LkC(k) — e(i), where eT fc > := (1, 1, . . . , 1) . The triangular system UkVl = Hk) remains to be solved. We wish to obtain y 9 = U k l e. ( k \ directly from y 9 k _ 1 . Using block Gaussian elimination, we find that since u k = ' U k .
What to read after Variational Analysis of Some Conjugate Gradient Methods?
You can find similar books in the "Read Also" column, or choose other free books by Daniel B Szyld to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
We first describe the method developed by Concus, Golub [5] and Widlund [46], which is commonly known as the CGW method. The Galerkin condition has the form (32) and, as in the symmetric, positive definite case, it is satisfied by x k — x = Vky k, where y 9 k is the solution of (68) V k T AV k yi = V k T r .
From (24), (28) and (67), it follows that (68) is equivalent to (69) Rk(I-Jk)y 9 k = Pie W .
We note that p t = (uj, Mv{) is the first element of the diagonal matrix R k and that we therefo...re can simplify equation (69) to (70) (I-J k )y 9 k = e (1) .
With the normalization given by (20), the LU factorization of (/ — J k ) = L k Uk requires no arithmetic; this is the reason for chosing (3 k in this way. The factors are i i r& i -i i i i -i i u k -72 03 -73 A >*+i 18 It is also easy to see that LkC(k) — e(i), where eT fc > := (1, 1, . . . , 1) . The triangular system UkVl = Hk) remains to be solved. We wish to obtain y 9 = U k l e. ( k \ directly from y 9 k _ 1 . Using block Gaussian elimination, we find that since u k = ' U k .
What to read after Variational Analysis of Some Conjugate Gradient Methods?
You can find similar books in the "Read Also" column, or choose other free books by Daniel B Szyld to read onlineMoreLess
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