Banded Matrices with Banded Inverses and A = LPU
نویسندگان
چکیده
Abstract. If A is a banded matrix with a banded inverse, then A = BC = F1 . . . FN is a product of block-diagonal matrices. We review this factorization, in which the Fi are tridiagonal and N is independent of the matrix size. For a permutation with bandwidth w, each Fi exchanges disjoint pairs of neighbors and N < 2w. This paper begins the extension to infinite matrices. For doubly infinite permutations, the factors F now include the left and right shift. For banded infinite matrices, we discuss the triangular factorization A = LPU (completed in a later paper on The Algebra of Elimination). Four directions for elimination give four factorizations LPU and UPL and U1πU2 (Bruhat) and L1πL2 with different L, U , P and π.
منابع مشابه
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