LANBPRO Lanczos bidiagonalization with partial reorthogonalization.
LANBPRO computes the Lanczos bidiagonalization of a real
matrix using the with partial reorthogonalization.
[U_k,B_k,V_k,R,ierr,work] = LANBPRO(A,K,R0,OPTIONS,U_old,B_old,V_old)
[U_k,B_k,V_k,R,ierr,work] = LANBPRO('Afun','Atransfun',M,N,K,R0, ...
OPTIONS,U_old,B_old,V_old)
Computes K steps of the Lanczos bidiagonalization algorithm with partial
reorthogonalization (BPRO) with M-by-1 starting vector R0, producing a
lower bidiagonal K-by-K matrix B_k, an N-by-K matrix V_k, an M-by-K
matrix U_k and a M-by-1 vector such that
A*V_k = U_k*B_k + R
Partial reorthogonalization is used to keep the columns of V_K and U_k
semiorthogonal:
MAX(DIAG((EYE(K) - V_K'*V_K))) <= OPTIONS.delta
and
MAX(DIAG((EYE(K) - U_K'*U_K))) <= OPTIONS.delta.
B_k = LANBPRO(...) returns the bidiagonal matrix only.
The first input argument is either a real matrix, or a string
containing the name of an M-file which applies a linear operator
to the columns of a given matrix. In the latter case, the second
input must be the name of an M-file which applies the transpose of
the same linear operator to the columns of a given matrix,
and the third and fourth arguments must be M and N, the dimensions
of then problem.
The OPTIONS structure is used to control the reorthogonalization:
OPTIONS.delta: Desired level of orthogonality
(default = sqrt(eps/K)).
OPTIONS.eta : Level of orthogonality after reorthogonalization
(default = eps^(3/4)/sqrt(K)).
OPTIONS.cgs : Flag for switching between different reorthogonalization
algorithms:
0 = iterated modified Gram-Schmidt (default)
1 = iterated classical Gram-Schmidt
OPTIONS.elr : If OPTIONS.elr = 1 (default) then extended local
reorthogonalization is enforced.
OPTIONS.onesided
: If OPTIONS.onesided = 0 (default) then both the left
(U) and right (V) Lanczos vectors are kept
semiorthogonal.
OPTIONS.onesided = 1 then only the columns of U are
are reorthogonalized.
OPTIONS.onesided = -1 then only the columns of V are
are reorthogonalized.
OPTIONS.waitbar
: The progress of the algorithm is display graphically.
If both R0, U_old, B_old, and V_old are provided, they must
contain a partial Lanczos bidiagonalization of A on the form
A V_old = U_old B_old + R0 .
In this case the factorization is extended to dimension K x K by
continuing the Lanczos bidiagonalization algorithm with R0 as a
starting vector.
The output array work contains information about the work used in
reorthogonalizing the u- and v-vectors.
work = [ RU PU ]
[ RV PV ]
where
RU = Number of reorthogonalizations of U.
PU = Number of inner products used in reorthogonalizing U.
RV = Number of reorthogonalizations of V.
PV = Number of inner products used in reorthogonalizing V.
References:
R.M. Larsen, Ph.D. Thesis, Aarhus University, 1998.
G. H. Golub & C. F. Van Loan, "Matrix Computations",
3. Ed., Johns Hopkins, 1996. Section 9.3.4.
B. N. Parlett, ``The Symmetric Eigenvalue Problem'',
Prentice-Hall, Englewood Cliffs, NJ, 1980.
H. D. Simon, ``The Lanczos algorithm with partial reorthogonalization'',
Math. Comp. 42 (1984), no. 165, 115--142.
Rasmus Munk Larsen, DAIMI, 1998.
没有合适的资源?快使用搜索试试~ 我知道了~
资源推荐
资源详情
资源评论
收起资源包目录
890329.zip (59个子文件)
新建文件夹
Accelerated Proximal Gradient
apg
__MACOSX
apg
._proximal_gradient_rpca.m 82B
._.DS_Store 82B
apg
.DS_Store 6KB
proximal_gradient_rpca.m 7KB
pos.m 48B
apg_partial
__MACOSX
apg_partial
._.DS_Store 82B
._partial_proximal_gradient_rpca.m 171B
apg_partial
.DS_Store 6KB
PROPACK
AtAfunc.m 224B
laneig.txt 2KB
helio.mat 250KB
lanpro.m 14KB
Atransfunc.m 232B
lanpro.txt 3KB
lanbpro.m 19KB
bdsqr_mex.c 2KB
mmwrite.m 6KB
bdsqr.mexglx 73KB
bdsqr.m 987B
laneig.doc 2KB
bdsqr.mexsol 94KB
tqlb.mexsg64 27KB
laneig.m 9KB
lanbpro.txt 3KB
bdsqr.mexw32 55KB
reorth.mexsg64 26KB
tqlb.mexglx 9KB
mmread.m 7KB
refinebounds.m 939B
compute_int.m 1KB
reorth.mexsg 25KB
dbdqr.f 445B
bdsqr.mexsg64 25KB
bdsqr.mexsg 25KB
lanbpro.doc 3KB
lansvd.m 9KB
reorth_mex.c 3KB
reorth.f 3KB
update_gbound.m 3KB
mminfo.m 3KB
lanpro.doc 3KB
lansvd.txt 2KB
reorth.m 3KB
tqlb.mexsg 25KB
reorth.mexglx 9KB
tqlb.f 5KB
tqlb.m 852B
test.m 9KB
pythag.m 618B
testtqlb.m 2KB
tqlb.mexsol 9KB
reorth.mexsol 85KB
lansvd.doc 2KB
Afunc.m 202B
Cfunc.m 293B
tqlb_mex.c 1KB
choosvd.m 560B
partial_proximal_gradient_rpca.m 8KB
pos.m 48B
共 59 条
- 1
gu5218
- 粉丝: 31
- 资源: 259
下载权益
C知道特权
VIP文章
课程特权
开通VIP
上传资源 快速赚钱
- 我的内容管理 展开
- 我的资源 快来上传第一个资源
- 我的收益 登录查看自己的收益
- 我的积分 登录查看自己的积分
- 我的C币 登录后查看C币余额
- 我的收藏
- 我的下载
- 下载帮助
安全验证
文档复制为VIP权益,开通VIP直接复制
信息提交成功
- 1
- 2
- 3
前往页