jwb@cepmax.ncsu.EDU (John W. Baugh Jr.) (07/01/90)
I'd like to find references to any work that's been done (particularly in the formal specification community) on specifying matrix operators, including tools, notations, etc. Also, it seems that the algebra of matrix elements has to be considered to do anything interesting with these specifications--are there any definitions of the "nice" properties that floating point representations are supposed to obey? Or perhaps all of this is just too messy--maybe the chasm between numerical analysis and linear algebra is too great. Any comments/suggestions welcome. John Baugh jwb@cepmax.ncsu.edu
steve@hubcap.clemson.edu ("Steve" Stevenson) (07/03/90)
jwb@cepmax.ncsu.EDU (John W. Baugh Jr.) writes: >Or perhaps all of this is just too messy--maybe the >chasm between numerical analysis and linear algebra >is too great. Any comments/suggestions welcome As a numerical analyst with lots of interests and experience in numerical linear algebra, I think you're missing much of the point. In any traditional sense, linear algebra is a major component of numerical. If you're restricting numerical to ``floating point'' then I suggest that you survey the literature a bit. Kahaner, who got the Turing Award This time, is just one of several schools of thought. For example, in Europe, there is a large following of Kuelish, et al, who center their work around making inner products work right---the rest follows from that. The interval people --- out at the Oregon Grad Center --- are also quite active. There is no chasm between numerical analysis and linear algebra --- they're intimately intertwined. -- =============================================================================== Steve (really "D. E.") Stevenson steve@hubcap.clemson.edu Department of Computer Science, (803)656-5880.mabell Clemson University, Clemson, SC 29634-1906
jwb@cepmax.ncsu.EDU (John W. Baugh Jr.) (07/03/90)
I write about specifying matrix operators. In article <9550@hubcap.clemson.edu>, steve@hubcap.clemson.edu ("Steve" Stevenson) writes: > As a numerical analyst with lots of interests and experience in numerical > linear algebra, I think you're missing much of the point. [stuff deleted] > There is no chasm between numerical analysis and linear algebra --- they're > intimately intertwined. Of course, I know that numerical analysis and linear algebra are "intimately intertwined." If you re-read my post you'll see that I'm talking about _specifying_matrix_operators_. My question regards the level at which such operators are specified. For example, if I write a program that happens to make use of matrices, I could take advantage of the "nice" algebraic properties of real numbers, and hence the matrices defined over them, to reason about my program. Of course, matrices of finite-precision numbers don't share these "nice" properties, which might encourage one to specify even more details, namely a floating point representation for matrix elements. The trouble is that pretty soon I'm at an "implementation" level, and I might just as well be writing Fortran code (since I'm specifying all these details anyway). The dramatic difference between these two levels of specification is the "chasm" I'm referring to. So, my question is: has any work been done in the area of specifying matrix operators? John Baugh jwb@cepmax.ncsu.edu