Determinant of a matrix
ALGORITHM
The determinant of an
LU decomposed matrix is the product of the diagonal elements. We can easy compute the determinant of a given matrix
A. by
LUDCMP function.
IMPLEMENTATION
Unit: fragment of a program
Interface: LUDCMP
Result:
the program displays the value of the determinant
/* read an input N by N matrix A. */
...
D = LUDCMP(N)
do J = 1 to N; D = D * A.J.J; end
say "Determinant =" D
|
EXAMPLE
The determinant of the input matrix A. (Combinatorial matrix)
A. = Y
do J = 1 to N
A.J.J = X + Y
end
|
is equal (X+N*Y)*X**(N-1). Computation of determinant for N=100, X=1, Y=2 and numeric digits 9 requires 17.57 seconds. The result is
Determinant = 201.001499
CONNECTIONS
Literature
Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P. Numerical Recipes in C : the art of scientific computing
- 2nd ed. University Press, Cambridge, 1992
Faddejev A.K., Sominskij J.S. Sbornik zadac po vyssej algebre
Nauka, Moskva 1964
