slarrk (3) - Linux Man Pages
subroutine slarrk (integerN, integerIW, realGL, realGU, real, dimension( * )D, real, dimension( * )E2, realPIVMIN, realRELTOL, realW, realWERR, integerINFO)
SLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy.
SLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy. This is an auxiliary code to be called from SSTEMR. To avoid overflow, the matrix must be scaled so that its largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest accuracy, it should not be much smaller than that. See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal Matrix", Report CS41, Computer Science Dept., Stanford University, July 21, 1966.
N is INTEGER The order of the tridiagonal matrix T. N >= 0.
IW is INTEGER The index of the eigenvalues to be returned.
GL is REAL
GU is REAL An upper and a lower bound on the eigenvalue.
D is REAL array, dimension (N) The n diagonal elements of the tridiagonal matrix T.
E2 is REAL array, dimension (N-1) The (n-1) squared off-diagonal elements of the tridiagonal matrix T.
PIVMIN is REAL The minimum pivot allowed in the Sturm sequence for T.
RELTOL is REAL The minimum relative width of an interval. When an interval is narrower than RELTOL times the larger (in magnitude) endpoint, then it is considered to be sufficiently small, i.e., converged. Note: this should always be at least radix*machine epsilon.
W is REAL
WERR is REAL The error bound on the corresponding eigenvalue approximation in W.
INFO is INTEGER = 0: Eigenvalue converged = -1: Eigenvalue did NOT converge
FUDGE REAL , default = 2 A "fudge factor" to widen the Gershgorin intervals.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
- September 2012
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