@article{2846136599ce4eb6bdc6e97d8edf0d52,

title = "Numerical solution to a linear equation with tensor product structure",

abstract = "We consider the numerical solution of a c-stable linear equation in the tensor product space ℝn1x...xnd, arising from a discretized elliptic partial differential equation in ℝd. 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(Σini)+O(ns) computational complexity, under appropriate assumptions (with ns being the flop count for solving a linear system associated with Ai-γIni). Illustrative numerical examples will be presented.",

keywords = "Cayley transform, elliptic partial differential equation, Kronecker product, large-scale problem, linear equation, Stein equation, Sylvester equation",

author = "Fan, {Hung Yuan} and Liping Zhang and Chu, {Eric King wah} and Yimin Wei",

note = "Funding Information: Ministry of Science and Technology, Taiwan, Grant/Award Number: MOST 105-2115-M-003-003; National Natural Science Foundation, China, Grant/Award Number: 11601484, 11271084; International Cooperation Project of Shanghai Municipal Science and Technology Commission, Grant/Award Number: 16510711200 Funding Information: The first author was supported by the Ministry of Science and Technology, Taiwan (Grant MOST 105-2115-M-003-003) and the second and fourth by the National Natural Science Foundation, China (Grants 11601484 and 11271084, respectively) the fourth author is also supported by the International Cooperation Project of Shanghai Municipal Science and Technology Commission (Grant No. 16510711200). Part of the work occurred when the second and third authors visited the School of Mathematical Sciences at Monash University and Fudan University, respectively. Funding Information: The first author was supported by the Ministry of Science and Technology, Taiwan (Grant MOST?105-2115-M-003-003) and the second and fourth by the National Natural Science Foundation, China (Grants 11601484 and 11271084, respectively) the fourth author is also supported by the International Cooperation Project of Shanghai Municipal Science and Technology Commission (Grant No. 16510711200). Part of the work occurred when the second and third authors visited the School of Mathematical Sciences at Monash University and Fudan University, respectively. Publisher Copyright: Copyright {\textcopyright} 2017 John Wiley & Sons, Ltd.",

year = "2017",

month = dec,

doi = "10.1002/nla.2106",

language = "English",

volume = "24",

journal = "Numerical Linear Algebra with Applications",

issn = "1070-5325",

publisher = "John Wiley and Sons Ltd",

number = "6",

}