1. A method of calculating numerical solutions of simultaneous linear equations by a simultaneous-linear-equations solving apparatus, said simultaneous linear equations having coefficient matrix elements and right-side vector elements, comprising the steps of: inputting, from an input apparatus, values of said coefficient matrix elements and values of said right-side vector elements of said simultaneous linear equations to be solved, storing said inputted values of said coefficient matrix elements and those of said right-side vector elements into a memory apparatus, a memory region for storing said inputted values of said coefficient matrix elements in said memory apparatus having a memory capacity capable of storing all of said coefficient matrix elements, creating a non-zero-structure-specifying index table for indicating a row number of a terminal-end non-zero element in each column and a column number of a terminal-end non-zero element in each row within said coefficient matrix, executing a decomposition processing toward said elements existing within a range indicated by said created index table, executing, based on said index table, a forward/backward substitution processing toward said coefficient matrix elements and said stored right-side vector elements, and thereby determining said numerical solutions, said coefficient matrix elements having been subjected to said decomposition processing, and outputting said determined numerical solutions from an output apparatus.