Numerical Algorithms
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Coiflets solutions for Föppl-von Kármán equations governing large deflection of a thin flat plate by a novel wavelet-homotopy approach
Numerical Algorithms - Tập 79 - Trang 993-1020 - 2018
In this paper, a novel technique incorporated the homotopy analysis method (HAM) with Coiflets is developed to obtain highly accurate solutions of the Föppl-von Kármán equations for large bending deflection. The characteristic scale transformation is introduced to nondimensionalize the governing equations. The results are obtained for the transformed nondimensional equations, which are in very exc......
Nonnegative surface fitting with Powell-Sabin splines
Numerical Algorithms - Tập 9 Số 2 - Trang 263-276 - 1995
On a nonlinear multigrid algorithm with primal relaxation for the image total variation minimisation
Numerical Algorithms - - 2006
Error bounds for septic Hermite interpolation and its implementation to study modified Burgers’ equation
Numerical Algorithms - - 2022
Circumcentering the Douglas–Rachford method
Numerical Algorithms - Tập 78 - Trang 759-776 - 2017
We introduce and study a geometric modification of the Douglas–Rachford method called the Circumcentered–Douglas–Rachford method. This method iterates by taking the intersection of bisectors of reflection steps for solving certain classes of feasibility problems. The convergence analysis is established for best approximation problems involving two (affine) subspaces and both our theoretical and nu......
Additive block diagonal preconditioning for block two-by-two linear systems of skew-Hamiltonian coefficient matrices
Numerical Algorithms - Tập 62 - Trang 655-675 - 2013
For a class of block two-by-two systems of linear equations with certain skew-Hamiltonian coefficient matrices, we construct additive block diagonal preconditioning matrices and discuss the eigen-properties of the corresponding preconditioned matrices. The additive block diagonal preconditioners can be employed to accelerate the convergence rates of Krylov subspace iteration methods such as MINRES......
Stabilized finite element method for the viscoelastic Oldroyd fluid flows
Numerical Algorithms - Tập 60 Số 1 - Trang 75-100 - 2012
Fast and Accurate Floating Point Summation with Application to Computational Geometry
Numerical Algorithms - Tập 37 - Trang 101-112 - 2004
We present several simple algorithms for accurately computing the sum of n floating point numbers using a wider accumulator. Let f and F be the number of significant bits in the summands and the accumulator, respectively. Then assuming gradual underflow, no overflow, and round-to-nearest arithmetic, up to ⌊2
F−f
/(1−2−f
)⌋+1 numbers can be accurately added by just summing the terms in decreasing o......
High-precision Gauss–Turán quadrature rules for Laguerre and Hermite weight functions
Numerical Algorithms - Tập 67 - Trang 59-72 - 2013
Procedures and corresponding Matlab software are presented for generating Gauss–Turán quadrature rules for the Laguerre and Hermite weight functions to arbitrarily high accuracy. The focus is on the solution of certain systems of nonlinear equations for implicitly defined recurrence coefficients. This is accomplished by the Newton–Kantorovich method, using initial approximations that are sufficien......
Implicit QR algorithms for palindromic and even eigenvalue problems
Numerical Algorithms - Tập 51 - Trang 209-238 - 2008
In the spirit of the Hamiltonian QR algorithm and other bidirectional chasing algorithms, a structure-preserving variant of the implicit QR algorithm for palindromic eigenvalue problems is proposed. This new palindromic QR algorithm is strongly backward stable and requires less operations than the standard QZ algorithm, but is restricted to matrix classes where a preliminary reduction to structure......
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