Appendix E. THOMAS ALGORITHM FOR MULTI-LAYERS OF VG MODEL

into a form:

where a_i's, b_i's, c_i's, and f_i's are give constants.b_i's and y_i'$s can be calculated by comparing corresponding elements of the above two equations, and x_i's can be expressed:

This equation can be solved by assuming: 

and obtaining a_i's, b_i's, and y_i's incrementally: 

Then x_i's can be obtained by a back substitution: