Shifted Kronecker Product Systems
نویسندگان
چکیده
Abstract. A fast method for solving a linear system of the form (A(p) ⊗ · · · ⊗ A(1) − λI)x = b is given where each A(i) is an ni-by-ni matrix. The first step is to convert the problem to triangular form (T (p) ⊗ · · · ⊗ T (1) − λI)y = c by computing the (complex) Schur decompositions of the A(i). This is followed by a recursive back-substitution process that fully exploits the Kronecker structure and requires just O(N(n1+ · · ·+np)) flops where N = n1 · · ·np. A similar method is employed when the real Schur Decomposition is used to convert each A(i) to quasi-triangular form. The numerical properties of these new methods are the same as if we explicitly formed (T (p) ⊗ · · · ⊗T (1) − λI) and used conventional back-substitution to solve for y.
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عنوان ژورنال:
- SIAM J. Matrix Analysis Applications
دوره 29 شماره
صفحات -
تاریخ انتشار 2006