Computing Reviews
Today's Issue Hot Topics Search Browse Recommended My Account Log In
Review Help
Search
Algorithm 993: efficient computation with Kronecker products
Fackler P. ACM Transactions on Mathematical Software45 (2):1-9,2019.Type:Article
Date Reviewed: Aug 14 2019

The Kronecker product of two matrices replaces each element of the first matrix with a multiple of a copy of the second matrix. The history, applications, and properties of the Kronecker and the symmetric products are well known [1,2]. For example, the Kronecker product is used in control theory to unfold systems of linear equations. In many applications, one needs to multiply a matrix represented as a Kronecker product of several matrices times an input matrix.

Are there more effective ways to compute this product than simply carrying out the Kronecker products, producing a large matrix, and then multiplying times the input matrix? Not surprisingly, the answer is yes. Fackler describes forward and backward algorithms for this problem, and shows how his methods can avoid the memory intensive matrix reordering required by other methods. He presents MATLAB implementations of his methods and compares them with previously implemented methods.

The major contributions of this research are algorithms to eliminate computationally intensive data shuffling, as well as a simplified way to optimally order the workflow. In light of the experimental results presented, I invite all algorithmic designers and MATLAB lovers to read this insightful paper and then recommend more diverse areas of Kronecker applications in more computing domains.

Reviewer:  Amos Olagunju Review #: CR146651 (1910-0372)
1) Schäcke, K. On the Kronecker product, master’s thesis. University of Waterloo, 2013, https://www.math.uwaterloo.ca/~hwolkowi/henry/reports/kronthesisschaecke04.pdf.
2) Zhang, H.; Ding, F. On the Kronecker products and their applications. Journal of Applied Mathematics 2013, (2013), Article ID 296185. http://dx.doi.org/10.1155/2013/296185.
Bookmark and Share
  Reviewer Selected
Featured Reviewer
 
 
Numerical Algorithms And Problems (F.2.1 )
 
 
Numerical Linear Algebra (G.1.3 )
 
 
Mathematical Software (G.4 )
 
Would you recommend this review?
yes
no
Other reviews under "Numerical Algorithms And Problems": Date
On the computational complexity of ordinary differential equations
Ko K. (ed) Information and Control 58(1-3): 157-194, 1984. Type: Article
Jun 1 1985
The computational complexity of simultaneous diophantine approximation problems
Lagarias J. SIAM Journal on Computing 14(1): 196-209, 1985. Type: Article
Jan 1 1986
Parallel and distributed computation: numerical methods
Bertsekas D., Tsitsiklis J., Prentice-Hall, Inc., Upper Saddle River, NJ, 1989. Type: Book (9789780136487005)
Apr 1 1990
more...

E-Mail This Printer-Friendly
Send Your Comments
Contact Us
Reproduction in whole or in part without permission is prohibited.   Copyright 1999-2024 ThinkLoud®
Terms of Use
| Privacy Policy