
MPI
 Referenced in 515 articles
[sw06496]
 dual numbers for second derivatives. Automatic differentiation techniques are typically derived based on the chain ... rule of differentiation. Other methods can be derived based on the inherent mathematical properties ... These methods are capable of producing effectively exact derivative values. However, when secondderivative information...

KELLEY
 Referenced in 631 articles
[sw04829]
 optimization of smooth functions. The methods studied in this first part rely on the availability ... first order, and sometimes also second order derivatives of the objective function. The first part ... Newton’s method, inexact Newton methods, and the GaussNewton method for the solution ... methods are sketched. The last chapter of the first part, chapter 5, studies projection methods...

ILUT
 Referenced in 170 articles
[sw08734]
 certain threshold. The second class of methods consists of techniques derived from modifications ... does not consider numerical values. The second is often far more expensive than the standard...

numDeriv
 Referenced in 62 articles
[sw11621]
 package provide methods for calculating (usually) accurate numerical first and second order derivatives. Accurate calculations ... applicable, a complex step derivative is available. A simple difference method is also provided. Simple...

SQPlab
 Referenced in 175 articles
[sw05161]
 other hand, as a Newton method, the SQP algorithm converges very rapidly, meaning that ... precision (this is particularly true when second derivatives are used). Therefore, one can say that ... defining the nonlinear optimization problem, and their derivatives, is time consuming. Indeed, in this case ... small number of iterations required by the method. If the rule above does not apply...

AD01
 Referenced in 15 articles
[sw12526]
 found. With the backward method, first and second derivatives are available...

Poblano
 Referenced in 12 articles
[sw04186]
 taking vector inputs. The gradient (i.e., first derivative) of the objective function is required ... optimizers. The optimization methods in Poblano include several nonlinear conjugate gradient methods (FletcherReeves, Polak ... memory quasiNewton method using BFGS updates to approximate secondorder derivative information ... truncated Newton method using finite differences to approximate secondorder derivative information...

CppAD
 Referenced in 36 articles
[sw04866]
 first and second derivatives of optimal values. The result is a method that yields large...

Optim
 Referenced in 17 articles
[sw29999]
 implemented routines for derivative free, firstorder, and secondorder optimization methods. The user...

numerov
 Referenced in 30 articles
[sw24970]
 Numerovtype methods is presented for the solution of some special second order Initial Value ... order conditions, we derive an optimal constant coefficients method along with a similar kind...

NEW9p
 Referenced in 28 articles
[sw24971]
 Numerovtype methods is presented for the solution of some special second order Initial Value ... order conditions, we derive an optimal constant coefficients method along with a similar kind...

CMAES
 Referenced in 120 articles
[sw05063]
 Strategy. Evolution strategies (ES) are stochastic, derivativefree methods for numerical optimization of nonlinear ... covariance matrix adaptation (CMA) is a method to update the covariance matrix of this distribution ... covariance matrix amounts to learning a second order model of the underlying objective function similar ... QuasiNewton method in classical optimization. In contrast to most classical methods, fewer assumptions...

LOCA
 Referenced in 33 articles
[sw04717]
 equations that describe the bifurcation. A Newton method is then formulated for this augmented system ... augmented system (a task that involved second derivatives and dense matrix rows), bordering algorithms ... that an application code using Newton’s method will already have invested in. Only...

PROC NLMIXED
 Referenced in 68 articles
[sw11039]
 approximate standard errors based on the second derivative matrix of the likelihood function. PROC NLMIXED ... approximate standard errors by using the delta method...

RIPPLE
 Referenced in 57 articles
[sw30642]
 force derived from the continuum surface force ( CSF) model. A twostep projection method ... advection is estimated with the weakly monotonic, second order upwind method of van Leer. Flow...

Algorithm 792
 Referenced in 36 articles
[sw04774]
 accuracy of new methods (or existing methods that are not included in this survey ... returns a value, first partials, and second partial derivatives of one of the test functions...

mfem
 Referenced in 47 articles
[sw22316]
 based on Lagrange multiplier techniques. The second, direct, approach (EBmfem) utilizes edgebasis functions ... CRmfem) utilizes the P1 nonconforming finite element method due to Crouzeix and Raviart and then ... this paper to derive, document, illustrate, and validate the three MATLAB implementations EBmfem, LMmfem...

KANTBP
 Referenced in 18 articles
[sw00482]
 secondorder ordinary differential equations which contain potential matrix elements and firstderivative coupling terms ... paper is to present the finite element method procedure based on the use of high...

SSPTSmethods
 Referenced in 7 articles
[sw38981]
 solution of hyperbolic PDEs. Multiderivative timestepping methods have recently been increasingly used ... coupled with forward Euler and a secondderivative formulation. However, many spatial discretizations ... stability properties when coupled with this secondderivative formulation, but rather with a more natural ... sufficient conditions for an explicit twoderivative multistage method to preserve the strong stability properties...

SERK2
 Referenced in 11 articles
[sw10426]
 SERK2v2: A new secondorder stabilized explicit RungeKutta method for stiff problems. Traditionally, explicit ... dimension. Stabilized RungeKutta methods (also called RungeKuttaChebyshev methods) were proposed ... these difficulties. The RungeKutta methods are explicit methods with extended stability domains, usually along ... Here, we develop a new method based on secondorder polynomials with...