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The LinearMatrixConsistency procedure

This procedure should be used in conjunction with RegularMatrix. It should be used only if the matrix includes rows or columns in which a variable appears with degree 1 in at least 2 elements of a row or a column. Its syntax is:

 
 LinearMatrixConsistency(A,VAR,vars,row,context,rohn,
                        Func,FuncKA,FuncAK,name)
The parameters are: Linearity has to be understood in a very loose sense. For example if a row of the matrix is
 
x    xy    x+y
this row may be considered as linear in x in which case we have 3 linear elements in the row. If the row is considered as linear in y we have 2 linear elements in the row. Note that the linearity is checked according to the order provided in Vars.

This procedure may be used for the matrix A, the conditioned matrix KA or the conditioned matrix AK. Context is used to indicate the choice according to the following code:

The complexity of this procedure is approximately $\prod (2^m_i)$ where $m_i$ is is the number of linear terms in the elements of row or column i of A. Hence it should not be be used with a large Vars. The use of Rohn matrix may also be expensive as it requires to calculate $2^(2n-1)$ scalar determinant, with $n$ the dimension of the matrix A.

For example we may use

 
LinearMatrixConsistency(A,[x,y],[x],1,5,"F","AKA","","Simp"):
In this example we will consider the row of matrix A and its elements that are linear in x. The procedure will be used for both the matrix A and the conditioned matrix KA (hence this procedure should be used with the parameter cond of RegularMAtrix set to 1 or 3. Note that we assume here that the conditioning matrix is ${\tt
A}^{-1}(Mid(X))$.


next up previous contents
Next: The GerschgorinConsistency procedure Up: Linear algebra Previous: The SpectralRadiusConsistency procedure   Contents
Jean-Pierre Merlet 2012-12-20