### On the Solution of Linear Algebraic Equations Involving Interval Coefficients (1996)On the Solution of Linear Algebraic Equations Involving Interval Coefficients (1996) Access Restriction
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 Author Markov, S. ♦ Popova, E. ♦ Ullrich, Ch. Source CiteSeerX Content type Text File Format PDF Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Interval Theta ♦ Real Matrix ♦ Directed Interval Matrix Algebra ♦ Linear Algebraic System Ax ♦ Simple Explicit Condition ♦ Interval Algebraic System Theta ♦ Interval Vector ♦ New Relation ♦ Mathematica Function ♦ Iteration Method ♦ Iterative Numerical Algorithm ♦ Special Case ♦ Initial Approximation ♦ Iterative Method ♦ Theta N-matrix ♦ Right-hand Side N-vector ♦ Different Problem ♦ Directed Interval ♦ Cramer-type Formula ♦ Improper Interval ♦ Interval Right-hand Side Description We discuss the solution to the interval algebraic system A \Theta x = b involving interval n \Theta n matrix A and interval vector b in directed interval arithmetic involving improper intervals. We give some new relations for directed intervals, which form the basis for a directed interval matrix algebra. Using such relations we prove convergence of an iterative method, formulated by L. Kupriyanova, under simple explicit conditions on the interval matrix A. We propose an iterative numerical algorithm for the solution to a class of interval algebraic systems A \Theta x = b. Cramer-type formula for a special case of real matrices and interval right-hand side are used for the computation of an initial approximation for the iteration method. A Mathematica function performing the proposed algorithm is described. 1 Introduction A linear algebraic system Ax = b involving intervals in the n \Theta n-matrix A and/or in the right-hand side n-vector b, relates to four different problems, resp. ... Educational Role Student ♦ Teacher Age Range above 22 year Educational Use Research Education Level UG and PG ♦ Career/Technical Study Learning Resource Type Article Publisher Date 1996-01-01 Publisher Institution In: S. Margenov, P. Vassilevski (Eds.): Iterative Methods in Linear Algebra, II, IMACS Series in Computational and Applied Mathematics