Title :
Abstract Matrix Arithmetic
Author :
Sexton, Alan P. ; Sorge, Volker ; Watt, Stephen M.
Author_Institution :
Univ. of Birmingham, Birmingham, UK
Abstract :
We present an approach to basic arithmetic between abstract matrices, i.e., matrices of symbolic dimension with underspecified components. We define a simple basis function that enables the representation of abstract matrices composed of arbitrary regions in a single term that supports matrix addition and multiplication by regular arithmetic on terms. This can, in particular, be exploited to obtain general arithmetic closure properties for classes of structured matrices. We also describe an approach using alternative basis functions that allow more compact expressions and admit additional arithmetic simplifications.
Keywords :
matrix algebra; abstract matrix arithmetic; alternative basis functions; general arithmetic closure properties; matrix addition; matrix multiplication; regular arithmetic; structured matrices; symbolic dimension; underspecified components; Arithmetic; Bismuth; Concrete; Europe; Genetic expression; Polynomials; Reduced instruction set computing; Scientific computing; abstract matrices; matrix computation; symbolic algebra;
Conference_Titel :
Symbolic and Numeric Algorithms for Scientific Computing, 2008. SYNASC '08. 10th International Symposium on
Conference_Location :
Timisoara
Print_ISBN :
978-0-7695-3523-4
DOI :
10.1109/SYNASC.2008.85