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SIAMSC
2008

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A Globally Convergent Numerical Method for a Coefficient Inverse Problem

13 years 4 months ago

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A survey of recent results of the authors is presented. This survey is short due to space limitations. A Coefficient Inverse Problem for a hyperbolic PDE with backscattering data ...

Larisa Beilina, Michael V. Klibanov

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Id	Views	Title	Status

1	245	A Globally Convergent Numerical Method for a Coefficient Inverse Problem	claim
2	237	A Variational Shape Optimization Approach for Image Segmentation with a Mumford--Shah Functional	claim
3	230	Augmented Mixed Finite Element Methods for the Stationary Stokes Equations	claim
4	206	The Compact Discontinuous Galerkin (CDG) Method for Elliptic Problems	claim
5	198	Model Reduction for Large-Scale Systems with High-Dimensional Parametric Input Space	claim
6	193	Exact and Approximate Sparse Solutions of Underdetermined Linear Equations	claim
7	192	Surface Mesh Smoothing, Regularization, and Feature Detection	claim
8	191	ORBIT: Optimization by Radial Basis Function Interpolation in Trust-Regions	claim
9	188	Adaptivity with Dynamic Meshes for Space-Time Finite Element Discretizations of Parabolic Equations	claim
10	187	The Generalized Singular Value Decomposition and the Method of Particular Solutions	claim
11	182	A Distributed SDP Approach for Large-Scale Noisy Anchor-Free Graph Realization with Applications to Molecular Conformation	claim
12	179	Multigrid Algorithms for Inverse Problems with Linear Parabolic PDE Constraints	claim
13	173	A Fast Iterative Method for Eikonal Equations	claim
14	168	Accurate Floating-Point Summation Part II: Sign, K-Fold Faithful and Rounding to Nearest	claim
15	167	High Order Numerical Quadratures to One Dimensional Delta Function Integrals	claim
16	167	Low-Dimensional Polytope Approximation and Its Applications to Nonnegative Matrix Factorization	claim
17	167	New Finite Elements for Large-Scale Simulation of Optical Waves	claim
18	165	Iterated Hard Shrinkage for Minimization Problems with Sparsity Constraints	claim
19	160	An Adaptive Multilevel Wavelet Solver for Elliptic Equations on an Optimal Spherical Geodesic Grid	claim
20	159	Hierarchical Clustering of Massive, High Dimensional Data Sets by Exploiting Ultrametric Embedding	claim
21	158	The Exact Computation of the Free Rigid Body Motion and Its Use in Splitting Methods	claim
22	151	Computing Ground States of Spin-1 Bose-Einstein Condensates by the Normalized Gradient Flow	claim
23	151	Accurate Floating-Point Summation Part I: Faithful Rounding	claim
24	150	Asymptotic Stability of a Jump-Diffusion Equation and Its Numerical Approximation	claim
25	149	Adaptive Discrete Galerkin Methods Applied to the Chemical Master Equation	claim
26	148	Multilevel Adaptive Aggregation for Markov Chains, with Application to Web Ranking	claim
27	147	Global and Finite Termination of a Two-Phase Augmented Lagrangian Filter Method for General Quadratic Programs	claim
28	146	A Continuous Interior Penalty Method for Viscoelastic Flows	claim
29	146	Long Time Numerical Solution of the Navier--Stokes Equations Based on a Sequential Regularization Formulation	claim
30	145	Fast Multilevel Algorithm for a Minimization Problem in Impulse Noise Removal	claim
31	143	Numerical Valuation of European and American Options under Kou's Jump-Diffusion Model	claim
32	142	A Fast Direct Solver for the Biharmonic Problem in a Rectangular Grid	claim
33	142	Multitarget Error Estimation and Adaptivity in Aerodynamic Flow Simulations	claim
34	142	Algebraic Multigrid Solvers for Complex-Valued Matrices	claim
35	140	Newton-GMRES Preconditioning for Discontinuous Galerkin Discretizations of the Navier--Stokes Equations	claim
36	140	Compact Fourier Analysis for Designing Multigrid Methods	claim
37	139	Probing the Pareto Frontier for Basis Pursuit Solutions	claim
38	136	On the Time Splitting Spectral Method for the Complex Ginzburg-Landau Equation in the Large Time and Space Scale Limit	claim
39	135	An Augmented Lagrangian Approach to Linearized Problems in Hydrodynamic Stability	claim
40	134	Efficient Solution of Anisotropic Lattice Equations by the Recovery Method	claim
41	133	Numerical Variational Methods Applied to Cylinder Buckling	claim
42	132	Stochastic Preconditioning for Diagonally Dominant Matrices	claim
43	131	Fast Monte Carlo Simulation Methods for Biological Reaction-Diffusion Systems in Solution and on Surfaces	claim
44	131	Gramian-Based Model Reduction for Data-Sparse Systems	claim
45	129	Bottom-Up Construction and 2: 1 Balance Refinement of Linear Octrees in Parallel	claim
46	129	Iterative Solution of Piecewise Linear Systems	claim
47	127	Restoration of Chopped and Nodded Images by Framelets	claim
48	127	On Diagonally Relaxed Orthogonal Projection Methods	claim
49	127	Fast (Structured) Newton Computations	claim
50	126	Highly Efficient Strong Stability-Preserving Runge-Kutta Methods with Low-Storage Implementations	claim
51	126	Towards a Statistical Theory of Texture Evolution in Polycrystals	claim
52	125	Hybrid Simulations of Reaction-Diffusion Systems in Porous Media	claim
53	123	Balanced Incomplete Factorization	claim
54	123	Adaptive Mesh Refinement for Nonparametric Image Registration	claim
55	122	A Framework for Discrete Integral Transformations II-The 2D Discrete Radon Transform	claim
56	118	Splitting Methods Based on Algebraic Factorization for Fluid-Structure Interaction	claim
57	117	Adaptive, Fast, and Oblivious Convolution in Evolution Equations with Memory	claim
58	116	A New Asymptotic Preserving Scheme Based on Micro-Macro Formulation for Linear Kinetic Equations in the Diffusion Limit	claim
59	115	A New Petrov--Galerkin Smoothed Aggregation Preconditioner for Nonsymmetric Linear Systems	claim
60	114	Inertia-Revealing Preconditioning For Large-Scale Nonconvex Constrained Optimization	claim
61	113	An Efficient and Robust Method for Simulating Two-Phase Gel Dynamics	claim
62	113	Limited Data X-Ray Tomography Using Nonlinear Evolution Equations	claim
63	113	Statistical Condition Estimation for the Roots of Polynomials	claim
64	111	Revisiting the Crowding Phenomenon in Schwarz-Christoffel Mapping	claim
65	111	An Algebraic Multigrid Approach Based on a Compatible Gauge Reformulation of Maxwell's Equations	claim
66	110	Numerical Coupling of Electric Circuit Equations and Energy-Transport Models for Semiconductors	claim
67	110	Large-Eddy Simulation of Thermal Flows based on Discrete-Velocity Models	claim
68	108	A Nine Point Scheme for the Approximation of Diffusion Operators on Distorted Quadrilateral Meshes	claim
69	108	Automated Code Generation for Discontinuous Galerkin Methods	claim
70	108	Symmetric Permutations for I-matrices to Delay and Avoid Small Pivots During Factorization	claim
71	107	A Hybrid Phase-Flow Method for Hamiltonian Systems with Discontinuous Hamiltonians	claim
72	106	Multilevel Linear Sampling Method for Inverse Scattering Problems	claim
73	106	Asynchronous Parallel Generating Set Search for Linearly Constrained Optimization	claim
74	106	Finite Volume Simulation of the Geostrophic Adjustment in a Rotating Shallow-Water System	claim
75	104	Deblurring Methods Using Antireflective Boundary Conditions	claim
76	104	Reducing Floating Point Error in Dot Product Using the Superblock Family of Algorithms	claim
77	99	Mixed Multiscale Finite Element Methods for Stochastic Porous Media Flows	claim
78	99	Monte Carlo Greeks for Financial Products via Approximative Transition Densities	claim
79	97	Numerical Methods for Computing Nonlinear Eigenpairs: Part II. Non-Iso-Homogeneous Cases	claim
80	97	Improvement of Space-Invariant Image Deblurring by Preconditioned Landweber Iterations	claim
81	97	Long-Time Simulations on High Resolution Meshes to Model Calcium Waves in a Heart Cell	claim
82	96	Stochastic Lie Group Integrators	claim
83	93	Stopping Criteria for Rational Matrix Functions of Hermitian and Symmetric Matrices	claim
84	92	On Multisymplecticity of Partitioned Runge-Kutta Methods	claim
85	92	A Novel Pricing Method for European Options Based on Fourier-Cosine Series Expansions	claim
86	90	Norm Preconditioners for Discontinuous Galerkin hp-Finite Element Methods	claim
87	87	Performance and Accuracy of LAPACK's Symmetric Tridiagonal Eigensolvers	claim
88	82	Dynamic Phase Boundaries for Compressible Fluids	claim
89	75	Well-Balanced Time Implicit Formulation of Relaxation Schemes for the Euler Equations	claim

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