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**:** 2013
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**:** . ., . . / . 43. .: , 2013. .78-94.

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** (.):** 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.

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