augmented matrix


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augmented matrix

[′ȯg·men·təd ′mā·triks]
(mathematics)
The matrix of the coefficients, together with the constant terms, in a system of linear equations.
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This system has solutions according to the KroneckerCapelli theorem (rank of this system augmented matrix and rank of this system basic matrix equal to 7).
Step 1 : Starting with the augmented matrix (A | B), reduce it to a form with an identity matrix of desired order, by elementary row operations only.
We thus start with the augmented matrix (A | B) and proceed as follows, using the indicated row operations:
For example, to compute a few of the smallest singular values, MATLAB's routine svds applies ARPACK [30, 39] to the augmented matrix M (1.
It appears that the augmented matrix formulation (1.
The program j dsvd [21, 22] implements a Jacobi-Davidson method on the augmented matrix formulation.
T] decomposition of the symmetric augmented matrix is computed using preprocessing that will help to minimize the fill-in during the factorization combined with one by one and two by two numerical pivot strategies [18, 17].
In Section 2, we will briefly summarize the approximation process and describe the basic properties of the linear system and augmented matrix.
where the elements of the matrices M and A of the augmented matrix of the left-hand side of (2.
1] after the row and column permutations, the augmented matrix in (2.
A portion of the singular values and vectors of a large sparse matrix A is computed in [12] by using a Jacobi-Davidson type method which makes use of the block structure of the augmented matrix

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