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The Inversion Problem for Computable Linear Operators
[chapter]
2003
Lecture Notes in Computer Science
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This is the inversion problem for computable linear operators on Banach spaces in its non-uniform and uniform formulation, respectively. ...
Given a program of a linear bounded and bijective operator T , does there exist a program for the inverse operator T −1 ? ...
Let
Conclusion We have investigated the non-uniform and the uniform version of the inversion problem for computable linear operators. ...
doi:10.1007/3-540-36494-3_35
fatcat:hgmqdhdyovcgnbpm4hs65eps2m
PyLops—A linear-operator Python library for scalable algebra and optimization
2020
SoftwareX
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Linear operators and optimization are at the core of many algorithms used in signal and image processing, remote sensing, and inverse problems. ...
However, many real-application, large-scale operators do not lend themselves to explicit matrix representations, usually forcing practitioners to forego the convenient linear-algebra syntax available for ...
The authors cannot be held liable for any inappropriate use of this software library. ...
doi:10.1016/j.softx.2019.100361
fatcat:2lq4wzab2bfgvgb3ertis7uv2u
A compiler for linear algebra operations
2016
Companion Proceedings of the 2016 ACM SIGPLAN International Conference on Systems, Programming, Languages and Applications: Software for Humanity - SPLASH Companion 2016
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In this paper we present a compiler that translates arithmetic expressions containing matrices to efficient sequences of calls to basic linear algebra kernels. ...
The Problem Linear algebra problems appear in fields as diverse as computational biology, finite element methods and control theory. ...
To deal with the inverse operator, in addition to computing X T X directly, different factorizations are applied to X. ...
doi:10.1145/2984043.2998539
dblp:conf/oopsla/Barthels16
fatcat:moxdr47onba3rpccxphibbine4
hIPPYlib: An Extensible Software Framework for Large-Scale Inverse Problems
2018
Journal of Open Source Software
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A computational framework for infinite-dimensional Bayesian inverse problems: Part II. Stochastic Newton MCMC with application to ice sheet inverse problems. ...
HIPPYlib: An extensible software framework for large-scale inverse problems; Part I: Deterministic inversion and linearized Bayesian inference. In preparation. ...
doi:10.21105/joss.00940
fatcat:z54j7jee7rbbpigas66lp7tpqq
Improving computational efficiency in large linear inverse problems: an example from carbon dioxide flux estimation
2013
Geoscientific Model Development
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This work proposes two approaches to lower the computational costs and memory requirements for large linear space–time inverse problems, taking the Bayesian approach for estimating carbon dioxide (CO<sub ...
For an examined benchmark problem, the two algorithms yielded massive savings in floating point operations relative to direct computation of the same quantities. ...
This material is based upon work supported by the National Aeronautics and Space Administration under Grant No. NNX12AB90G and the National Science Foundation under Grant No. 1047871. Edited by: L. ...
doi:10.5194/gmd-6-583-2013
fatcat:c46rnus3q5gntoeanyanjhsr3q
Page 3925 of Mathematical Reviews Vol. , Issue 91G
[page]
1991
Mathematical Reviews
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A mollifier method for linear operator equations of the first kind. Inverse Problems 6 (1990), no. 3, 427-440. ...
Summary: “In this paper an inversion method for the solution of ill-posed linear problems is presented. ...
On Linear Representation, Complexity and Inversion of maps over finite fields
[article]
2022
arXiv
pre-print
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2020 pre-print arXiv:2010.14601v1 fatcat:zklgiguno5bpfh4gatm62ql3faOther Versions
The paper primarily addressed the problem of linear representation, invertibility, and construction of the compositional inverse for non-linear maps over finite fields. ...
The linear representation, defined over the space of functions, naturally defines a notion of linear complexity for non-linear maps, which can be viewed as a measure of computational complexity associated ...
The formula for inverse of a map F solves the problem of computing the inverse image x given y = F (x). Hence the problem of computing the inverse image is weaker than computing the inverse formula. ...
arXiv:2010.14601v4
fatcat:hvyat7spb5gi3c3sf7mixhcuoe
Optimal Experimental Design for Infinite-dimensional Bayesian Inverse Problems Governed by PDEs: A Review
[article]
2021
arXiv
pre-print
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2020 pre-print arXiv:2005.12998v2 fatcat:y2kujbn5b5abhocm2qp4axqfniOther Versions
We present the mathematical foundations of OED in this context and survey the computational methods for the class of OED problems under study. ...
We present a review of methods for optimal experimental design (OED) for Bayesian inverse problems governed by partial differential equations with infinite-dimensional parameters. ...
Thanks also to Noémi Petra for helpful discussions and feedback. I am grateful to Karina Koval for carefully reading through a draft of this article and for help with proofreading. ...
arXiv:2005.12998v3
fatcat:x2aeba2l4fh7ph6vlhw5zfpqke
A multilevel ℌ-matrix-based approximate matrix inversion algorithm for vectorless power grid verification
2013
2013 18th Asia and South Pacific Design Automation Conference (ASP-DAC)
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For most of the existing vectorless verification algorithms, the subproblem of linear system solution which computes the inverse of the power grid matrix takes up a large part of the computation time and ...
Experimental results have shown that the proposed algorithm can obtain an almost linear complexity both in runtime and memory consumption for efficient vectorless power grid verification. ...
If we use preconditioned conjugate gradient (PCG) methods to compute the corresponding row of the inverse matrix for each node, the whole linear system solution may take up about 80% of the computation ...
doi:10.1109/aspdac.2013.6509590
dblp:conf/aspdac/ZhaoCY13
fatcat:bb3vhyqmjzg4ticch2nnawtef4
Technical Note: Improving computational efficiency in large linear inverse problems: an example from carbon dioxide flux estimation
2012
Geoscientific Model Development Discussions
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This work proposes two approaches to lower the computational costs and memory requirements for large linear space-time inverse problems, taking the Bayesian approach for estimating car-10 bon dioxide ( ...
Such estimation problems often represent inverse problems that are formulated as linear optimization problems. ...
This material is based upon work supported by the National Aeronautics ...
doi:10.5194/gmdd-5-3325-2012
fatcat:qlptmz6urzdndlxtu3snjndyei
Invariant imbedding and inverse problems with applications to radiative transfer
1999
Computers and Mathematics with Applications
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The first method involves two auxiliary integro-differential equations. The inverse problem is solved by a sequence of approximation solutions of linear equations. ...
ln this paper, we developed two methods to solve the inverse problem of a nonlinear integro-differential equation. Both methods are based on the principle of invariant imbedding. ...
And, in Section 4, the problem is reduced to computing inverses of a 2n x 2n matrix and computing under operators. All of the above procedures can be carried out on a large or parallel computer. ...
doi:10.1016/s0898-1221(99)00149-2
fatcat:3efdhqlk2vb57hwj3huob2nxby
hIPPYlib: An Extensible Software Framework for Large-Scale Inverse Problems Governed by PDEs; Part I: Deterministic Inversion and Linearized Bayesian Inference
[article]
2020
arXiv
pre-print
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algorithms for PDE-based inverse problems that exploit the structure of the underlying operators, notably the Hessian of the log-posterior. ...
The key property of the algorithms implemented in hIPPYlib is that the solution of the deterministic and linearized Bayesian inverse problem is computed at a cost, measured in linearized forward PDE solves ...
ACKNOWLEDGMENTS e authors would like to thank Georg Stadler for providing very helpful comments on an earlier version of this paper. ...
arXiv:1909.03948v2
fatcat:mslipsg4onhtlcpe7evjqi2j6y
Page 4781 of Mathematical Reviews Vol. , Issue 86j
[page]
1986
Mathematical Reviews
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This paper deals with iterative methods for the linear operator equation (*) Az = b, where A is a linear, bounded, selfadjoint and nonnegative operator (i.e., (Az, z) > 0 for all z) in a Hilbert space ...
This paper is a continuation of part I [see the preceding review]. The authors establish lower bounds for iterative procedures for solving linear ill-posed operator equations. ...
Regularization networks for inverse problems: A state-space approach
2003
Automatica
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An analytic expression is provided for the basis functions as well as for the entries of the matrix of the linear system used to compute the weights. ...
Linear inverse problems with discrete data are equivalent to the estimation of the continuous-time input of a linear dynamical system from samples of its output. ...
The main aim of the present paper is to provide an algorithm for the computation of the activation functions η i (t) that holds for linear inverse problems admitting a state-space representation. ...
doi:10.1016/s0005-1098(02)00280-7
fatcat:uecosjtwenetvldl2c3ccwxjvm
A Class of Generalized Approximate Inverse Solvers for Unsymmetric Linear Systems of Irregular Structure Based on Adaptive Algorithmic Modelling for Solving Complex Computational Problems in Three Space Dimensions
2016
Applied Mathematics
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in complex computational problems in three space dimensions. ...
A class of general inverse matrix techniques based on adaptive algorithmic modelling methodologies is derived yielding iterative methods for solving unsymmetric linear systems of irregular structure arising ...
problems in parallel computer environments. ...
doi:10.4236/am.2016.711108
fatcat:vqf3zrfcebasbcsxc427h4e5lu
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