Rigorous solution of linear programming problems with uncertain data

This note gives a synopsis of new methods for solving linear systems and linear programming problems with uncertain data. All input data can vary between given lower and upper bounds. The methods calculate very sharp and guaranteed error bounds for the solution set of those problems and permit a rigorous sensitivity analysis. For problems with exact input data in general the calculated bounds differ only in the last bit in the mantissa, i.e. they are of maximum accuracy.