The evaluation of linear forms

This presentation deals with the evaluation and transformation of linear forms. Especial emphasis is given to implicit methods in which it is not necessary to find the explicit values,x _i . The relation of the Aitken triple product matrixCA ^–1 B to the result of a linear transformation of linear forms is noted, and the numerical computation of this triple product matrix is indicated with the use of the simple Abbreviated Doolittle solution. Application is also made to the evaluation ofA ^–1 and ofA ^–1 C.