NAG Fortran Library Routine Document E04KYF
ثبت نشده
چکیده
A typical iteration starts at the current point x where nz (say) variables are free from both their bounds. The projected gradient vector gz, whose elements are the derivatives of F ðxÞ with respect to the free variables, is known. A unit lower triangular matrix L and a diagonal matrix D (both of dimension nz), such that LDL is a positive-definite approximation of the matrix of second derivatives with respect to the free variables (i.e., the projected Hessian) are also held. The equations
منابع مشابه
NAG Fortran Library Routine Document E04MFF=E04MFA
Note: this routine uses optional parameters to define choices in the problem specification and in the details of the algorithm. If you wish to use default settings for all of the optional parameters, you need only read Section 1 to Section 9 of this document. Refer to the additional Section 10, Section 11 and Section 12 for a detailed description of the algorithm, the specification of the optio...
متن کاملNAG Fortran Library Routine Document E04NKF=E04NKA
Note: this routine uses optional parameters to define choices in the problem specification and in the details of the algorithm. If you wish to use default settings for all of the optional parameters, you need only read Section 1 to Section 9 of this document. Refer to the additional Section 10, Section 11 and Section 12 for a detailed description of the algorithm, the specification of the optio...
متن کاملNAG Fortran Library Routine Document E02BEF
where Ni x ð Þ denotes the normalized cubic B-spline defined upon the knots i; iþ1; . . . ; iþ4. The total number n of these knots and their values 1; . . . ; n are chosen automatically by the routine. The knots 5; . . . ; n 4 are the interior knots; they divide the approximation interval x1; xm 1⁄2 into n 7 subintervals. The coefficients c1; c2; . . . ; cn 4 are then determined as the solution...
متن کاملNAG Fortran Library Routine Document E02BAF
In order to define the full set of B-splines required, eight additional knots 1; 2; 3; 4 and nþ4; nþ5; nþ6; nþ7 are inserted automatically by the routine. The first four of these are set equal to the smallest xr and the last four to the largest xr. The representation of sðxÞ in terms of B-splines is the most compact form possible in that only nþ 3 coefficients, in addition to the nþ 7 knots, fu...
متن کاملNAG Fortran Library Routine Document C02AGF
The routine generates a sequence of iterates z1; z2; z3; . . ., such that jP ðzkþ1Þj < jP ðzkÞj and ensures that zkþ1 þ Lðzkþ1Þ ‘roughly’ lies inside a circular region of radius jF j about zk known to contain a zero of P ðzÞ; that is, jLðzkþ1Þj jF j, where F denotes the Féjer bound (see Marden (1966)) at the point zk. Following Smith (1967), F is taken to be minðB; 1:445nRÞ, where B is an upper...
متن کامل