In the fig. 88
the program is aimed for approximation (smoothing) a tabular dependence of a
function of two arguments: the function is given by user but the program gives
its coefficients.

We have considered the same function for solution
one-dimensional problem in T tip 81: fig. 88.
But it evolution of the problem in the fig. 81
for two-dimensional problem[1].

Initial tabular data are noted
in a matrix M in the fig. 88.
Empty places in the matrix are elements that equal infinity (10^{307})
and have the style “in white and white” but not empty place of the sparse matrix
(the operator of input the matrix M is duplicated on pink
background so that all its elements were visible). When we decompose the matrix
M
on the vectors X, Y and Z the given
“infinite” elements are ignored. So in the fig. 88
there are thirty initial elements in the matrix M (5 lines and 6
columns), but there 25 elements in the vectors X, Y and Z.

By this fig. 88 we finish the series of tips that touch
the theme “Invisible symbol on the display”. Such symbol helps us:

·
to have blank as the symbol of the sum operator[2]
(the tip 13);

·
to introduce into calculations invisible functions and, for example, to
simulate “Roman” arithmetic with help of them (the tip 19);

·
to output the value of zero dimensional variable sine unit of measure (the
tip 60);

·
to work with degree Celsius and Fahrenheit degree without any problems (the
tip 64);

·
to leave out the description of Boolean constant in infinite cycle (see
first function Root in the fig. 84);

·
to add empty programming lines for separation the line’s group of
operators in Mathcad-programs (for it
we write some numerical constant with the style “in white and white” on the
line);

·
to simulate sparse matrixes and vectors (fig. 88).