ICT100 to ICT105

ICT100 to ICT105 are taken from Numerische Mathematik. These procedures were provided by Dr Natha.

ICT100

            procedure reduction(n,a,b,dl,fail);
value n;
integer n;
array a,b,dl;
label fail;

Reduction of the general symmetric eigenvalue with the symmetric matrix Ax = λBx, with the symmetric matrix A and symmetric positive definite matrix B, to the equivalent standard problem Pz = λz.

Ref: Numerische Mathematik 11,99-110 (1968), procedure reduce 1.

ICT101

            procedure rator(n,m,posdef,dlam,eps,d,b2);
value n,m,posdef,dlam,eps;
integer n,m;
Boolean posdef;
real dlam,eps;
array d,b2;

QR algorithm for the computation of the lowest eigenvalues of a symmetric tridiagonal matrix.

Ref: Numerische Mathematik 11, 264-272 (1968).

ICT102

            procedure tred(n,tol,a,d,e,e2);
value n,tol;
integer n;
real tol;
array a,d,e,e2;

This procedure reduces the given lower triangle of a symmetric matrix, to tridiagonal form using Householder's reduction.

Ref: Numerische Mathematik 11,181-195 (1968), procedure tred 1

ICT103

            procedure tridiinverseiteration(c,b,n,w,norm,m1,macheps,z);
value n,m1,norm,macheps;
integer n,m1;
real norm,macheps;
array c,b,w,z;

This procedure calculates the eigenvectors of a symmetric tridiagonal matrix by inverse iteration, given very accurate eigenvalues.

Ref: Numerische Mathematik 4, 368-376 (1962).

ICT104

            procedure backtransformation(a,b,x,n,m1);
value n,m1;
integer n,m1;
array a,b,z;

This procedure calculates the eigenvectors of the original symmetric matrix A, from those eigenvectors of the tridiagonal matrix which were computed by ICT103.

Ref: Numerische Mathematik 4, 354-361 (1962).

ICT105

            procedure bisect(c,beta,n,m1,m2,eps1,relfeh,eps2,z,x);
value n,m1,m2,eps1,relfeh;
real eps1,eps2,relfeh;
integer n,m1,m2;
array c,b,x,beta;

This procedure calculates the eigenvalues of a symmetric tridiagonal matrix by the method of bisection.

Ref: Numerische Mathematik 9, 386-393 (1967).