Numerical solution to a linear equation with tensor product structure

作者：Fan, Hung-Yuan; Zhang, Liping^*; Chu, Eric King-wah; Wei, Yimin

来源：Numerical Linear Algebra with Applications, 2017, 24(6): e2106.

DOI：10.1002/nla.2106

• Cayley transform
• elliptic partial differential equation
• Kronecker product
• large-scale problem
• linear equation
• Stein equation
• Sylvester equation

We consider the numerical solution of a c-stable linear equation in the tensor product space R-n1x . . .xnd, arising from a discretized elliptic partial differential equation in R-d. Utilizing the stability, we produce an equivalent d-stable generalized Stein-like equation, which can be solved iteratively. For large-scale problems defined by sparse and structured matrices, the methods can be modified for further efficiency, producing algorithms of O(Sigma(i)n(i)) + O(n(s)) computational complexity, under appropriate assumptions (with n(s) being the flop count for solving a linear system associated with (A(i) - gamma I-ni). Illustrative numerical examples will be presented.

• 出版日期2017-12
• 单位浙江工业大学; 复旦大学