Determinant of a block-triangular matrix A block-upper-triangular matrix is a matrix of the form where and are square matrices. PropositionLet be a block-upper-triangular matrix, as defined above. Then, Proof A block-lower-triangular matrix is a matrix of the form where and are square matric...
We try to design two numerical algorithms by a certain type of matrix reordering in matrix partition and another algorithm by using the transformation of a block upper triangular transformation for the cyclic heptadiagonal Toeplitz matrices. The cost of these algorithms is about 11n+O(logn) for ...
The dspsv function performs the factorization A=UDU’, where U is a unitriangular matrix and D is a block diagonal matrix where the blocks are of dimension 1×1 or 2×2. In addition to the solution for x, the dspsv function also returns the matrices U and D. The matrix D may then...
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