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Ill-posed

Ill-Posed Problems

Ill-Posed Problems

... If, alternatively, s is a small positive number, then the exponent 2 + 5 is large and the solution y1(t) at t = 1 will be a very large number; this number will be the larger the smaller is s. For s → 0 (i.e., for m → 3), ...

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OPTIMAL CONTROL FOR A CONTROLLED ILL-POSED WAVE EQUATION WITHOUT REQUIRING THE SLATER HYPOTHESIS

OPTIMAL CONTROL FOR A CONTROLLED ILL-POSED WAVE EQUATION WITHOUT REQUIRING THE SLATER HYPOTHESIS

... To sum up, our work leads to solving the optimal control problem for an ill-posed wave equation without requiring the extra hypothesis of Slater. The main idea was to make a null controllability approach to ...

11

No-Regret Optimal Control Characterization for an Ill-Posed Wave Equation

No-Regret Optimal Control Characterization for an Ill-Posed Wave Equation

... of ill-posed problems are not generally regular then its characterization may be different of standard optimal control ...an ill-posed wave problem (instable ...

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Expanding the applicability of Lavrentiev regularization methods for ill-posed problems

Expanding the applicability of Lavrentiev regularization methods for ill-posed problems

... an ill-posed problem in a Hilbert space setting using the Lavrentiev regularization method and, in particular, expanding the applicability of this method by weakening the popular Lipschitz-type hypotheses ...

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Regularization of ill posed mixed variational inequalities with non monotone perturbations

Regularization of ill posed mixed variational inequalities with non monotone perturbations

... In this paper, we study a regularization method for ill-posed mixed variational inequalities with non-monotone perturbations in Banach spaces. The convergence and convergence rates of regularized solutions ...

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Identification of source term for the ill posed Rayleigh–Stokes problem by Tikhonov regularization method

Identification of source term for the ill posed Rayleigh–Stokes problem by Tikhonov regularization method

... In this paper, we study an inverse source problem for the Rayleigh–Stokes problem for a generalized second-grade fluid with a fractional derivative model. The problem is severely ill-posed in the sense of ...

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A modified quasi-boundary value method for a class of abstract parabolic ill-posed problems

A modified quasi-boundary value method for a class of abstract parabolic ill-posed problems

... We study a final value problem for first-order abstract differential equation with posi- tive self-adjoint unbounded operator coefficient. This problem is ill-posed. Perturbing the final condition, we obtain ...

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A New Regularized Solution to Ill Posed Problem in Coordinate Transformation

A New Regularized Solution to Ill Posed Problem in Coordinate Transformation

... solving ill-posed problems in coordinate trans- formation through modifying small singular ...of ill-posed problems, and gain an applicable precision, moreover, perform stronger ...

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An Application of Newton Type Iterative Method for Lavrentiev Regularization for Ill-Posed Equations: Finite Dimensional Realization

An Application of Newton Type Iterative Method for Lavrentiev Regularization for Ill-Posed Equations: Finite Dimensional Realization

... of ill-posed equations. Precisely we consider the ill-posed equation F (x) = f when the available data is f δ with kf − f δ k ≤ δ and the operator F : D(F ) ⊆ X → X is a nonlinear monotone ...

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An optimal order yielding discrepancy principle for simplified regularization of ill posed problems in Hilbert scales

An optimal order yielding discrepancy principle for simplified regularization of ill posed problems in Hilbert scales

... an ill-posed operator equation T x = y, where T is a bounded linear operator between Hilbert ...the ill-posedness of the equation and smoothness of the ...

13

The Significance of Solutions Obtained from Ill Posed Systems of Linear Equations Constituted by Synchrotron Radiation Based Anomalous Small Angle X Ray Scattering

The Significance of Solutions Obtained from Ill Posed Systems of Linear Equations Constituted by Synchrotron Radiation Based Anomalous Small Angle X Ray Scattering

... of ill-posed ASAXS equations prevent- ing matrix inversion have been ...extremely ill-posed ASAXS problems avoiding inversion and the use of direct methods for in- stance Gaussian ...

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On Improving the Semilocal Convergence of Newton-Type Iterative Method for Ill-posed Hammerstein Type Operator Equations

On Improving the Semilocal Convergence of Newton-Type Iterative Method for Ill-posed Hammerstein Type Operator Equations

... Abstract—George and Pareth( 2012), presented a quartically convergent Two Step Newton type method for approximately solving an ill-posed operator equation in the finite dimensional setting of Hilbert ...

7

On the control of ill-posed distributed parameter
systems

On the control of ill-posed distributed parameter systems

... Abstract. We show that the so-called low-regret (or least-regret) control by J. L. Lions [8] fits on the control of ill-posed problems. At each time, we give the characterization of the so-called no-regret ...

17

Ill-Posed Point Neuron Models

Ill-Posed Point Neuron Models

... Abstract We show that point-neuron models with a Heaviside firing rate function can be ill posed. More specifically, the initial-condition-to-solution map might be- come discontinuous in finite time. ...

21

Ill-Posed and Linear Inverse Problems

Ill-Posed and Linear Inverse Problems

... Abstract. In this paper ill-posed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it’s relation to the kernel, is described. For ...

8

Regularization of Ill-Posed Point Neuron Models

Regularization of Ill-Posed Point Neuron Models

... Abstract Point neuron models with a Heaviside firing rate function can be ill-posed. That is, the initial-condition-to-solution map might become discontinuous in finite time. If a Lipschitz continuous but ...

23

An iterative regularization method for an abstract ill-posed biparabolic problem

An iterative regularization method for an abstract ill-posed biparabolic problem

... In this work we extend this method to our ill-posed biparabolic problem. To the best of our knowledge, the literature devoted to this class of problems is quite scarce, except the paper []. The study of ...

17

Numerical methods for ill-posed, linear problems

Numerical methods for ill-posed, linear problems

... R., ''Some Numerical Results for the Solution of the Heat Equation Backwards in Time," Numerical Solutions of Nonlinear Differential Equations.. and Hilbert D., Methods of Mathematical P[r] ...

130

Regularization of nonlinear Ill-posed equations with accretive operators

Regularization of nonlinear Ill-posed equations with accretive operators

... [2] , Metric and generalized projection operators in Banach spaces: Properties and applica- tions, Theory and Applications of Nonlinear Operators of Accretive and Monotone Type (A. Karts[r] ...

23

A discrete model for an ill-posed nonlinear parabolic PDE

A discrete model for an ill-posed nonlinear parabolic PDE

... ÒQÙQËtÏ<áNÛhËtÏ×[Ï×0ÎSÚ0Ë^è,ÎDÓBã,ÎDÙQÖ`ÎSÉGÝrÊ%ÏÓ%Î`Ê%Ê`àIVXWAY Z ÔoÞ É6ÚQÎ`Í^Ë/ÙQã;Ê¢ÏÓ%Î`ÊBÊ>Ìá[Ï×QÎèGÎ`ÖDÏBÉ,Ó[Y Z E]\^VDC`_abVcCa àQË^Ù. Ûh×QË^Ö×\ Ë/Ê4ÏB×QÎ=émÐ(ÏÓBËâcÓBÎ`È0ÓB[r] ...

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