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Convex interval interpolation with cubic splines, II
Springer Science and Business Media LLC - Tập 31 - Trang 328-340 - 1991
The problem of convex interval interpolation with cubicC
1-splines has an infinite number of solutions, if it is solvable at all. For selecting one of the solutions a regularized mean curvature is minimized. The arising finite dimensional constrained program is solved numerically by means of a dualization approach.
An application of Chawla's identity to a different scheme for singular problems
Springer Science and Business Media LLC - Tập 30 - Trang 566-568 - 1990
Evalquote in simple Fortran: A tutorial on interpreting Lisp
Springer Science and Business Media LLC - Tập 12 - Trang 299-317 - 1972
This paper describes the implementation of a pedagogical version of Evalquote with a set of Fortran subroutines. Their study enables the user to understand the programming machinery needed to interpret Lisp programs; the implementation of the subroutines allows him to run pure Lisp in machines for which only Fortran is available. The approach used in this paper is to define a stack-machine capable......
Two new approaches for solving elliptic obstacle problems using discontinuous Galerkin methods
Springer Science and Business Media LLC - Tập 62 - Trang 89-124 - 2021
The main aim of this article is to present two new ways to solve the elliptic obstacle problem by using discontinuous Galerkin finite element methods. In Gaddam and Gudi (Comput Methods Appl Math 18:223–236, 2018.
https://doi.org/10.1515/cmam-2017-0018......
Accurate discretization of poroelasticity without Darcy stability
Springer Science and Business Media LLC - Tập 61 - Trang 941-976 - 2021
In this manuscript we focus on the question: what is the correct notion of Stokes–Biot stability? Stokes–Biot stable discretizations have been introduced, independently by several authors, as a means of discretizing Biot’s equations of poroelasticity; such schemes retain their stability and convergence properties, with respect to appropriately defined norms, in the context of a vanishing storage c......
A simplified HSS preconditioner for generalized saddle point problems
Springer Science and Business Media LLC - Tập 56 - Trang 423-439 - 2015
For generalized saddle point problems, we propose a simplified Hermitian and skew-Hermitian splitting (SHSS) preconditioner which is much closer to the generalized saddle point matrix than the HSS preconditioner. It is proved that all eigenvalues of the SHSS preconditioned matrix are real and nonunit eigenvalues are located in a positive interval. We also study the eigenvector distribution and the......
Parallel Newton Two-Stage Multisplitting Iterative Methods for Nonlinear Systems
Springer Science and Business Media LLC - Tập 43 - Trang 849-861 - 2003
Parallel Newton two-stage iterative methods to solve nonlinear systems are studied. These algorithms are based on both the multisplitting technique and the two-stage iterative methods. Convergence properties of these methods are studied when the Jacobian matrix is either monotone or an H-matrix. Furthermore, in order to illustrate the performance of the algorithms studied, computational results ab......
Fractional Tikhonov regularization for linear discrete ill-posed problems
Springer Science and Business Media LLC - Tập 51 - Trang 197-215 - 2011
Tikhonov regularization is one of the most popular methods for solving linear systems of equations or linear least-squares problems with a severely ill-conditioned matrix A. This method replaces the given problem by a penalized least-squares problem. The present paper discusses measuring the residual error (discrepancy) in Tikhonov regularization with a seminorm that uses a fractional power of the......
Solving sparse linear systems by an abs-method that corresponds toLU-decomposition
Springer Science and Business Media LLC - Tập 28 - Trang 709-718 - 1988
Abaffy, Broyden, and Spedicato (ABS) have recently proposed a class of direct methods for solving nonsparse linear systems. It is the purpose of this paper to demonstrate that with proper choice of parameters, ABS methods exploit sparsity in a natural way. In particular, we study the choice of parameters which corresponds to an LU-decomposition of the coefficient matrix. In many cases, the fill-in......
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