Efficiently finding a single row of the inverse of a symmetric (not Hermitian) complex matrix
up vote
0
down vote
favorite
I want to find, at many frequencies $w$, the response at a few nodes to input at one node in a 1-D kinematic system with constraints, i.e. find (part of) $mathbf x$ s.t. $$left(- w^2 mathbf M + jw mathbf C + mathbf Kright) mathbf x = [1,0,0,...]^T$$
where, due to already comprehending the constraint equations, $mathbf M$, $mathbf C$, and $mathbf K$ are all real symmetric, on the order of 10 x 10, but not n- or block-diagonal, or sparse enough to be helpful. $mathbf M$ is positive definite, but the others (and the resulting complex matrix) are not.
Question 1:
Is there some way to take advantage of the symmetry (similar to Cholesky) and/or the limited number of required outputs?
Question 2:
Is there some way to incrementally advance a solution for changing $w$?
numerical-linear-algebra symmetric-matrices
asked Nov 16 at 16:47
TrollShadowknight
13
add a comment |
up vote
0
down vote
favorite
I want to find, at many frequencies $w$, the response at a few nodes to input at one node in a 1-D kinematic system with constraints, i.e. find (part of) $mathbf x$ s.t. $$left(- w^2 mathbf M + jw mathbf C + mathbf Kright) mathbf x = [1,0,0,...]^T$$
where, due to already comprehending the constraint equations, $mathbf M$, $mathbf C$, and $mathbf K$ are all real symmetric, on the order of 10 x 10, but not n- or block-diagonal, or sparse enough to be helpful. $mathbf M$ is positive definite, but the others (and the resulting complex matrix) are not.
Question 1:
Is there some way to take advantage of the symmetry (similar to Cholesky) and/or the limited number of required outputs?
Question 2:
Is there some way to incrementally advance a solution for changing $w$?
numerical-linear-algebra symmetric-matrices
asked Nov 16 at 16:47
TrollShadowknight
13
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I want to find, at many frequencies $w$, the response at a few nodes to input at one node in a 1-D kinematic system with constraints, i.e. find (part of) $mathbf x$ s.t. $$left(- w^2 mathbf M + jw mathbf C + mathbf Kright) mathbf x = [1,0,0,...]^T$$
where, due to already comprehending the constraint equations, $mathbf M$, $mathbf C$, and $mathbf K$ are all real symmetric, on the order of 10 x 10, but not n- or block-diagonal, or sparse enough to be helpful. $mathbf M$ is positive definite, but the others (and the resulting complex matrix) are not.
Question 1:
Is there some way to take advantage of the symmetry (similar to Cholesky) and/or the limited number of required outputs?
Question 2:
Is there some way to incrementally advance a solution for changing $w$?
numerical-linear-algebra symmetric-matrices
asked Nov 16 at 16:47
TrollShadowknight
13
I want to find, at many frequencies $w$, the response at a few nodes to input at one node in a 1-D kinematic system with constraints, i.e. find (part of) $mathbf x$ s.t. $$left(- w^2 mathbf M + jw mathbf C + mathbf Kright) mathbf x = [1,0,0,...]^T$$
where, due to already comprehending the constraint equations, $mathbf M$, $mathbf C$, and $mathbf K$ are all real symmetric, on the order of 10 x 10, but not n- or block-diagonal, or sparse enough to be helpful. $mathbf M$ is positive definite, but the others (and the resulting complex matrix) are not.
Question 1:
Is there some way to take advantage of the symmetry (similar to Cholesky) and/or the limited number of required outputs?
Question 2:
Is there some way to incrementally advance a solution for changing $w$?
numerical-linear-algebra symmetric-matrices
numerical-linear-algebra symmetric-matrices
asked Nov 16 at 16:47
TrollShadowknight
13
asked Nov 16 at 16:47
TrollShadowknight
13
edited 2 days ago
asked Nov 16 at 16:47
TrollShadowknight
13
asked Nov 16 at 16:47
TrollShadowknight
13
asked Nov 16 at 16:47
TrollShadowknight
13
13
add a comment |
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3001360%2fefficiently-finding-a-single-row-of-the-inverse-of-a-symmetric-not-hermitian-c%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
