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