exact soultion of full interval linear equation ax=b based on kaucher arithmetic

Exact soultion of full interval linear equation AX=B based on Kaucher arithmetic

Algebraic approach to the interval linear static identification, tolerance, and control problems, or one more application of kaucher arithmetic

In this paper, the ident(fitzahm probl~n, the tolermu:e probl~n, and the amtrol problon are treated for the interval linear equation A z = b. These problems require computing ;in inner approximatiem of the unitM .~h,ion. sa E s ~ ( A , b) = {x E R n I (3A ~ A ) ( A x ~ b ) } , f the tolerable sohaion .~et ~vS(A, b ) = {x R '~ ] (VA E A ) ( A x ~ b)} , and of the cmmoltabte.~dtaion.*a E ~ v ( A ...

Interval Linear Programming with generalized interval arithmetic

Generally, vagueness is modelled by a fuzzy approach and randomness by a stochastic approach. But in some cases, a decision maker may prefer using interval numbers as coefficients of an inexact relationship. In this paper, we define a linear programming problem involving interval numbers as an extension of the classical linear programming problem to an inexact environment. By using a new simple...

Exact real arithmetic for interval number systems

An interval number system is given by an initial interval cover of the extended real line and by a finite system of nonnegative Möbius transformations. Each sequence of transformations applied to an initial interval determines a sequence of nested intervals whose intersection contains a unique real number. We adapt in this setting exact real algorithms which compute arithmetical operations to a...

Interval methods that are guaranteed to underestimate (and the resulting new justification of Kaucher arithmetic)

One of the main objectives of interval computations is. given the function f(zx . . . . , a:n). and n intervals x l , . . . , x n , to compute the range ~ --f ( x l , . . . , x n ) . Traditional methods of interval arithmetic compute an mM, a'ure Y _D # fi~r the desired interval :9, an end(tsure that is often an overestimatilm. It is desirable to know how dose this enck~sure is to the desired r...

Iterative solutions to the linear matrix equation AXB + CXTD = E

In this paper the gradient based iterative algorithm is presented to solve the linear matrix equation AXB +CXD = E, where X is unknown matrix, A,B,C,D,E are the given constant matrices. It is proved that if the equation has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. Two numerical examples show that the introduced iterative a...