14 research outputs found
Constrained Hardy Space Approximation
We consider the problem of minimizing the distance kf − kLp(K), where K is a subset of the complex unit circle @D and ∈ C(K), subject
to the constraint that f lies in the Hardy space Hp(D) and |f| ≤ g for
some positive function g. This problem occurs in the context of filter
design for causal LTI systems. We show that the optimization problem
has a unique solution, which satisfies an extremal property similar to that
for the Nehari problem. Moreover, we prove that the minimum of the
optimization problem can be approximated by smooth functions. This
makes the problem accessible for numerical solution, with which we deal
in a follow-up paper
Constrained Hardy Space Approximation II: Numerics
We consider the problem of minimizing the distance kf − kLp(K), where K is a subset of the complex unit circle @D and ∈ C(K), subject
to the constraint that f lies in the Hardy space Hp(D) and |f| ≤ g for
some positive function g. This problem occurs in the context of filter
design for causal LTI systems. We show that the optimization problem
has a unique solution, which satisfies an extremal property similar to that
for the Nehari problem. Moreover, we prove that the minimum of the
optimization problem can be approximated by smooth functions. This
makes the problem accessible for numerical solution, with which we deal
in a follow-up paper
Convergence of an adaptive hp finite element strategy in higher space-dimensions
We develop a general convergence analysis for a class of inexact Newton-type regularizations for stably solving nonlinear ill-posed problems. Each of the methods under consideration consists of two components: the outer Newton iteration and an inner regularization scheme which, applied to the linearized system, provides the update. In this paper we give a novel and unified convergence analysis which is not confined to a specific inner regularization scheme but applies to a multitude of schemes including Landweber and steepest decent iterations, iterated Tikhonov method, and method of conjugate gradients
An hp-Efficient Residual-Based A Posteriori Error Estimator for Maxwell\u27s Equations
We develop a general convergence analysis for a class of inexact Newton-type regularizations for stably solving nonlinear ill-posed problems. Each of the methods under consideration consists of two components: the outer Newton iteration and an inner regularization scheme which, applied to the linearized system, provides the update. In this paper we give a novel and unified convergence analysis which is not confined to a specific inner regularization scheme but applies to a multitude of schemes including Landweber and steepest decent iterations, iterated Tikhonov method, and method of conjugate gradients
On Reduced Models For The Chemical Master Equation
We develop a general convergence analysis for a class of inexact Newton-type regularizations for stably solving nonlinear ill-posed problems. Each of the methods under consideration consists of two components: the outer Newton iteration and an inner regularization scheme which, applied to the linearized system, provides the update. In this paper we give a novel and unified convergence analysis which is not confined to a specific inner regularization scheme but applies to a multitude of schemes including Landweber and steepest decent iterations, iterated Tikhonov method, and method of conjugate gradients
A primal-dual finite element approximation for a nonlocal model in plasticity
We develop a general convergence analysis for a class of inexact Newton-type regularizations for stably solving nonlinear ill-posed problems. Each of the methods under consideration consists of two components: the outer Newton iteration and an inner regularization scheme which, applied to the linearized system, provides the update. In this paper we give a novel and unified convergence analysis which is not confined to a specific inner regularization scheme but applies to a multitude of schemes including Landweber and steepest decent iterations, iterated Tikhonov method, and method of conjugate gradients
Boundary Element Approximation for Maxwell\u27s Eigenvalue Problem
We develop a general convergence analysis for a class of inexact Newton-type regularizations for stably solving nonlinear ill-posed problems. Each of the methods under consideration consists of two components: the outer Newton iteration and an inner regularization scheme which, applied to the linearized system, provides the update. In this paper we give a novel and unified convergence analysis which is not confined to a specific inner regularization scheme but applies to a multitude of schemes including Landweber and steepest decent iterations, iterated Tikhonov method, and method of conjugate gradients
Convergence of an Automatic hp-Adapative Finite Elemet Strategy for Maxwell\u27s Equations
We develop a general convergence analysis for a class of inexact Newton-type regularizations for stably solving nonlinear ill-posed problems. Each of the methods under consideration consists of two components: the outer Newton iteration and an inner regularization scheme which, applied to the linearized system, provides the update. In this paper we give a novel and unified convergence analysis which is not confined to a specific inner regularization scheme but applies to a multitude of schemes including Landweber and steepest decent iterations, iterated Tikhonov method, and method of conjugate gradients
Geometric Reconstruction in Bioluminescence Tomography
We develop a general convergence analysis for a class of inexact Newton-type regularizations for stably solving nonlinear ill-posed problems. Each of the methods under consideration consists of two components: the outer Newton iteration and an inner regularization scheme which, applied to the linearized system, provides the update. In this paper we give a novel and unified convergence analysis which is not confined to a specific inner regularization scheme but applies to a multitude of schemes including Landweber and steepest decent iterations, iterated Tikhonov method, and method of conjugate gradients
Efficient simulation of discrete stochastic reaction systems with a splitting method
We develop a general convergence analysis for a class of inexact Newton-type regularizations for stably solving nonlinear ill-posed problems. Each of the methods under consideration consists of two components: the outer Newton iteration and an inner regularization scheme which, applied to the linearized system, provides the update. In this paper we give a novel and unified convergence analysis which is not confined to a specific inner regularization scheme but applies to a multitude of schemes including Landweber and steepest decent iterations, iterated Tikhonov method, and method of conjugate gradients