• # 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 second-derivative 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 Gauss-Newton 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...
• # 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 (Fletcher-Reeves, Polak ... memory quasi-Newton method using BFGS updates to approximate second-order derivative information ... truncated Newton method using finite differences to approximate second-order derivative information...
• # numerov

• Referenced in 30 articles [sw24970]
• Numerov-type 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]
• Numerov-type 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...
• # CMA-ES

• Referenced in 120 articles [sw05063]
• Strategy. Evolution strategies (ES) are stochastic, derivative-free methods for numerical optimization of non-linear ... 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 ... Quasi-Newton 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 two-step 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 edge-basis 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]
• second-order ordinary differential equations which contain potential matrix elements and first-derivative 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. Multi-derivative time-stepping methods have recently been increasingly used ... coupled with forward Euler and a second-derivative formulation. However, many spatial discretizations ... stability properties when coupled with this second-derivative formulation, but rather with a more natural ... sufficient conditions for an explicit two-derivative multistage method to preserve the strong stability properties...
• # SERK2

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