PURPOSE: To increase the calculation speed by referring to an index table to perform forth/back-substitution calculation in a forth/back-substitution part by the parallel processing and controlling repeat calculation including the forth/back-substitution calculation by a repeat calculation part to calculate an approximate solution of simulta neous linear equations.

CONSTITUTION: A forth/back-substitution part 2 subjects the coefficient vector inputted through a repeat calculation part 3 to the inverse matrix operation of an approximate matrix generated by a coefficient matrix decomposing part 1 and outputs the result to the repeat calculation part 3. The forth/back-substitution part 2 refers to the index table generated in an index generating part 4 to perform the forth/back-substitution calculation by the parallel processing, and the repeat calculation part 3 controls the repeat calculation including the forth/back-subsitution calculation to calculate an approximate solution of simultaneous linear equations. Consequently, the calculation in forth/back-substitution part 2 for the inverse matrix operation of the approximate matrix is performed by the parallel processing because the index table preliminarily generated by the index generating part 4 is used. Thus, the parallel calculation processing is performed in the repeat calculation including the forth/back-substitution calculation to quickly calculate the approximate solution of simultaneous linear equations.