" "
" "


:   . ., . .
:  
:  43
:  
:  2013
:   . ., . . / . 43. .: , 2013. .78-94.
:   , , ,
(.):  interval linear equation set, pseudo-solution of interval equation set, Linear programming, exact computations
:   Ax=b, A b. tol(A,b)={x:Ax2b}. ol(A,b(z))= {x:Ax=(1 z)b)}, z =inf{z: tol(A,b(z))6=;}. tol(A,b(z )) . , . , . - . ( MPI), GPU ( CUDA C).
(.):  We consider a set of linear equations Ax=b with
interval matrices A, b. Solutions are items of tol(A,b)={x: A?x2
? b}. Let
tol(A,b(z))={x: Ax=(1+z)b)}, z

=
inf{z:
tol(A,b(z))6=
;
}
be.
Items of the set tol(A,b(z )) are referred to as pseudosolutions.
We prove existence of a pseudosolution for all sets of interval
algebraic linear equations, suggest a technique to search for the
pseudosolution via solving the corresponding linear programming
problem. The obtained problem is singular, thus computations demand
accuracy exceeding that of standard data types of programming
languages. Simplex method coupled with errorless rational-fractional
computations gives an efficient solution of the problem. Coarsegrained
parallelism for distributed computer systems with MPI gives
a software implementation tool. CUDA C software is suggested for
errorless rational-fractional calculations.

PDF
-

: 4099, : 1412, : 14.


© 2007.