Exploiting the underdetermined system in multichannel active noise control for open windows 著者: He, Jianjun, Lam, Bhan, Shi, Dongyuan, Gan, Woon Seng

“…Therefore, we could leverage the underdetermined system to simplify the ANC system without degrading the noise reduction performance. …”
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Double descent in the condition number 著者: Poggio, Tomaso, Kur, Gil, Banburski, Andrzej

“…An overdetermined system (n>d) and especially an underdetermined system (n<d), for which the pseudoinverse must be used instead of the inverse, typically have significantly better, that is lower, condition numbers. …”
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Implicit regularization for optimal sparse recovery 著者: Vaškevičius, T, Kanade, V, Rebeschini, P

“…We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under the restricted isometry assumption. …”

Fourth-Order Spline Methods For Solving Nonlinear Schrödinger Equation 著者: Ahmad, Azhar

“…Since the methods result in an underdetermined system, the supplementary initial and boundary conditions are used to solve the system. …”
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Performance Comparisons of Greedy Algorithms in Compressed Sensing 著者: Blanchard, J, Tanner, J

“…Compressed sensing has motivated the development of numerous sparse approximation algorithms designed to return a solution to an underdetermined system of linear equations where the solution has the fewest number of nonzeros possible, referred to as the sparsest solution. …”

Proximal variable metric method with spectral diagonal update for large scale sparse optimization 著者: Woo, Gillian Yi Han, Sim, Hong Seng, Goh, Yong Kheng, Leong, Wah June

“…We will tackle the l0-norm sparse optimization problem using an underdetermined system as a constraint in this research. …”

On the number of Hadamard matrices via anti-concentration 著者: Ferber, Asaf, Jain, Vishesh, Zhao, Yufei

“…Many problems in combinatorial linear algebra require upper bounds on the number of solutions to an underdetermined system of linear equations Ax=b , where the coordinates of the vector x are restricted to take values in some small subset (e.g. {±1} ) of the underlying field. …”
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Performance comparisons of greedy algorithms in compressed sensing 著者: Blanchard, J, Tanner, J

“…Compressed sensing has motivated the development of numerous sparse approximation algorithms designed to return a solution to an underdetermined system of linear equations where the solution has the fewest number of nonzeros possible, referred to as the sparsest solution. …”

Random matching pursuit for image watermarking 著者: Hua, Guang, Zhao, Lifan, Zhang, Haijian, Bi, Guoan, Xiang, Yong

“…The classical solution to an underdetermined system of linear equations mainly has two opposite directions, which lead to either a large ℓ 2 -norm sparse solution or a non-sparse minimum ℓ 2 -norm solution. …”
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When Compressive Sensing Meets Data Hiding 著者: Hua, Guang, Xiang, Yong, Bi, Guoan

“…Unlike the conventional orthonormal full-space dictionary, the over-complete dictionary produces an underdetermined system with infinite transform results. We first discuss the minimum norm formulation (ℓ2-norm) which yields a closed-form solution and the concept of watermark projection, so that higher embedding capacity and an additional privacy preserving feature can be obtained. …”
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Performance comparisons of greedy algorithms in compressed sensing 著者: Blanchard, J, Tanner, J

“…Compressed sensing has motivated the development of numerous sparse approximation algorithms designed to return a solution to an underdetermined system of linear equations where the solution has the fewest number of nonzeros possible, referred to as the sparsest solution. …”

Numerical computation-based position estimation for QR code object marker: mathematical model and simulation 著者: Teoh, Mooi Khee, Teo, Kenneth Tze Kin, Yoong, Hou Pin

“…The three-dimensional (3D) positional information can be extracted from the underdetermined system using the QR code’s four vertices as positioning points. …”
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Acquisition and reconstruction techniques for improving rapid magnetic resonance imaging with applications in fetal imaging 著者: Arefeen, Yamin I.(Yamin Ishraq)

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Splines For Two-Dimensional Partial Differential Equations 著者: Abd Hamid, Nur Nadiah

“…By adding the initial and boundary conditions, an underdetermined system of linear equations results. This system is then solved using the method of Least Squares. …”
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Monocular vision-based position detection of qr marker using numerical computation 著者: Teoh, Mooi Khee

“…The four vertices of the QR code are used as the positioning points to determine the 3D information from the underdetermined system with two known parameters, camera’s focal length and QR code’s dimension. …”
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QuadPlus : design, modeling, and receding horizon-based control of a hyperdynamic quadrotor 著者: Singh, Karanjot, Mehndiratta, Mohit, Feroskhan, Mir

“…Moreover, a novel cascade approach comprising of a high-level nonlinear model predictive control (NMPC) algorithm is adopted to obtain the optimal actuator configuration for an underdetermined system while dealing with the physical constraints. …”
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A Monte Carlo method to estimate cell population heterogeneity from cell snapshot data 著者: Lambert, B, Gavaghan, DJ, Tavener, SJ

“…Our method is appropriate for underdetermined systems, where there are fewer distinct types of observations than parameters to be determined, and where observed variation is mostly due to variability in cellular processes rather than experimental measurement error. …”