“…In this study, PBPK model parameters for CP‐I were estimated using the cluster Gauss–Newton method (CGNM), an algorithm used to find multiple approximate solutions for nonlinear least‐squares problems. …”
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“…Furthermore, parameter estimation in WB-PBPK models may cause overfitting when applying to individual clinical data such as urine/feces drug excretion for each patient in which Cluster Newton Method (CNM) is applicable for parameter estimation. …”
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“…This book shows the importance of studying semilocal convergence in iterative methods through Newton's method and addresses the most important aspects of the Kantorovich's theory including implicated studies. …”
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“…Mathematical Review and Computer Arithmetic Mathematical Review Computer Arithmetic Interval ComputationsNumerical Solution of Nonlinear Equations of One Variable Introduction Bisection Method The Fixed Point Method Newton's Method (Newton-Raphson Method) The Univariate Interval Newton MethodSecant Method and Müller's Method Aitken Acceleration and Steffensen's Method Roots of Polynomials Additional Notes and SummaryNumerical Linear Algebra Basic Results from Linear Algebra Normed Linear Spaces Direct Methods for Solving Linear SystemsIterative Methods for Solving Linear SystemsThe Singular Value DecompositionApproximation TheoryIntroduction Norms, Projections, Inner Product Spaces, and Orthogonalization in Function SpacesPolynomial ApproximationPiecewise Polynomial ApproximationTrigonometric ApproximationRational ApproximationWavelet BasesLeast Squares Approximation on a Finite Point SetEigenvalue-Eigenvector Computation Basic Results from Linear Algebra The Power Method The Inverse Power Method Deflation The QR Method Jacobi Diagonalization (Jacobi Method) Simultaneous Iteration (Subspace Iteration)Numerical Differentiation and Integration Numerical Differentiation Automatic (Computational) Differentiation Numerical IntegrationInitial Value Problems for Ordinary Differential Equations Introduction Euler's Method Single-Step Methods: Taylor Series and Runge-Kutta Error Control and the Runge-Kutta-Fehlberg Method Multistep Methods Predictor-Corrector Methods Stiff Systems Extrapolation Methods Application to Parameter Estimation in Differential EquationsNumerical Solution of Systems of Nonlinear Equations Introduction and Fréchet Derivatives Successive Approximation (Fixed Point Iteration) and the Contraction Mapping Theorem Newton's Method and VariationsMultivariate Interval Newton MethodsQuasi-Newton Methods (Broyden's Method)Methods for Finding All SolutionsOptimization Local OptimizationConstrained Local Optimization Constrained Optimization and Nonlinear Systems Linear ProgrammingDynamic Programming Global (Nonconvex) OptimizationBoundary-Value Problems and Integral Equations Boundary-Value Problems Approximation of Integral EquationsAppendix: Solutions to Selected ExercisesReferencesIndexExercises appear at the end of each chapter.…”
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“…In multiphase (≥3) equilibrium calculations, when the Newton method is used to solve the material balance (Rachford-Rice) equations, poorly conditioned Jacobian can lead to false convergence. …”
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“…The feasibility of this framework was demonstrated by developing a new algorithm based on the Cluster Newton method, namely the constrained Cluster Newton method, where the initial points of the parameters are constrained by the database. …”
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“…Harper explores the ways in which Newton's method aims to turn theoretical questions into ones which can be answered empirically by measurement from phenomena, and to establish that propositions inferred from phenomena are provisionally accepted as guides to further research. …”
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“…Compared with the traditional forward Newton method, the total iteration time of the improved forward Newton method is reduced in the subpixel iteration stage, and the computational efficiency is 3.8 times that of the traditional NR algorithm. …”
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“…Other machine learning methods were comparable with the deterministic Gauss-Newton method and with each other.…”
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“…Two approaches are known for solving large-scale unconstrained optimization problems—the limited-memory quasi-Newton method (truncated Newton method) and the conjugate gradient method. …”
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“…Computer Number Systems and Floating Point Arithmetic Introduction Conversion from Base 10 to Base 2Conversion from Base 2 to Base 10Normalized Floating Point SystemsFloating Point OperationsComputing in a Floating Point SystemFinding Roots of Real Single-Valued Functions Introduction How to Locate the Roots of a Function The Bisection Method Newton's Method The Secant MethodSolving Systems of Linear Equations by Gaussian Elimination Mathematical Preliminaries Computer Storage for Matrices. …”
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“…The book highlights methods such as the steepest descent method, Newton method, conjugate direction method, conjugate gradient methods, quasi-Newton methods, rank one correction formula, DFP method, BFGS method and their algorithms, convergence analysis, and proofs. …”
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“…Some basic concepts and Smale's theory for Newton's method, together with its modifications and higher-order methods, are presented in the first two chapters. …”
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“…That is among others extending the classical Newton method theory which requires usual differentiability of function. …”
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“…INTRODUCTION AND TOOLSA Survey About Inverse Scattering TheoryBasic Definitions and ToolsDIRECT SCATTERING PROBLEMSAcoustic Obstacle ScatteringThe Inhomogeneous Acoustic MediumElectromagnetic Scattering by a Perfect ConductorThe Electromagnetic Inhomogeneous MediumScattering by Orthotropic MediaAnisotropic Electromagnetic MediaUNIQUENESS AND STABILITY IN INVERSE SCATTERINGAcoustic ScatteringElectromagnetic ScatteringTHE CASE OF FINITE DATAFinite Data in Inverse Acoustic ScatteringInverse Electromagnetic ScatteringTHE POINT-SOURCE METHOD AND APPLICATIONSReconstruction Of Acoustic ScattersInverse Electromagnetic Scattering Reconstruction of the Boundary Values of Scattered FieldsConvergence of a Regularized Newton MethodSINGULAR SOURCES AND SHAPE RECONSTRUCTIONAcoustic ScatteringElectromagnetic ScatteringLINEAR SAMPLING METHODSThe Original Linear Sampling MethodSpectral Theory and a Modified Linear Sampling MethodShape Reconstruction for Orthotropic MediaAnisotropic Electromagnetic MediaREFERENCESINDEX.…”
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“…It is observed that our method is superior to Newton's method and other sixth order methods considered.…”
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“…The proposed algorithm has faster convergence speed than the existing first-order methods and distributed Newton method. Experimental results have demonstrated the effectiveness of our proposed approach.…”
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“…Examples of nuggets include Newton's method, the irrationality of π, Bernoulli numbers, and the Gamma function. …”
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“…Finally, the minimization problem is solved by a quasi-Newton method to estimate DOA. Simulation results show that our algorithm has some advantages over most existing methods: it needs a small number of snapshots to estimate DOA, while the number of sources need not be known a priori. …”
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“…The comparisons are given with some other newly developed sixteenth-order methods. Interval Newton's method is also used for finding the enough accurate initial approximations. …”
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