A least squares approach for saddle point problems

Karaduman, Gül; Yang, Mei; Li, Ren-Cang

doi:10.1007/s13160-022-00509-y

Cited by 4 publications

(2 citation statements)

References 11 publications

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“…To improve the efficiency of the method, we can use a restart strategy that resets the momentum term and the matrix to their initial values after a certain number of iterations [10,11]. This can help avoid getting trapped in local minima and accelerate convergence to the global minimum of the function.…”

Section: Evaluating the Functions Of Symmetric Matrix Using Restarted...mentioning

confidence: 99%

Polynomial-Based Approach for Efficient Function Computation of Symmetric Matrices Using Restarted Heavy Ball Method

Karaduman¹

2023

ICPIS

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This paper presents a polynomial-based approach for efficiently computing functions ofsymmetric matrices by leveraging the Restarted Heavy Ball (RHB) method. The RHB method is employedto overcome the slow convergence issue commonly encountered when computing functions of symmetricmatrices. The key idea of our approach is to approximate the desired function using a polynomial. Byrepresenting the function as a polynomial, we can leverage the efficient computation of polynomials toaccelerate the overall function computation process. We introduce a systematic methodology forconstructing an optimal polynomial approximation that minimizes the approximation error. To furtherenhance the convergence speed, we incorporate the Restarted Heavy Ball method into our polynomialbased approach. The Restarted Heavy Ball iteration is applied after a certain number of iterations to resetthe computation process and mitigate the slow convergence behavior. The experimental results and analysisvalidate the effectiveness and practicality of our approach, highlighting its potential for various applicationsinvolving function computations of symmetric matrices. Overall, our polynomial-based approach,integrated with the Restarted Heavy Ball method, offers an efficient and accurate solution for computingfunctions of symmetric matrices. The experimental results and analysis validate the effectiveness andpracticality of our approach, highlighting its potential for various applications involving functioncomputations of symmetric matrices.

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Section: Evaluating the Functions Of Symmetric Matrix Using Restarted...mentioning

confidence: 99%

Polynomial-Based Approach for Efficient Function Computation of Symmetric Matrices Using Restarted Heavy Ball Method

Karaduman¹

2023

ICPIS

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“…However, this method suffers from slow convergence and numerical instability. In contrast, iterative methods require less computational time and storage space [7,8]. Iterative approaches, such as matrix iterations of the form 𝑋 𝑘+1 = 𝑓(𝑋 𝑘 ), where f represents a polynomial or a rational function, present appealing alternatives for square root computations.…”

Section: Introductionmentioning

confidence: 99%

Streamlining Square Root Matrix Function Computation with Restarted Heavy Ball Algorithm

Karaduman

2023

Journal of Engineering Technology and Applied Sciences

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This research proposes a new efficient algorithm for calculating the square root function of the large-scale nonsingular sparse matrix by restarting the Heavy Ball Algorithm. The square root matrix function is critical in various applications, including signal processing, image processing, and machine learning. However, its computation is challenging due to existing methods' high computational complexity and numerical instability. The restarted Heavy Ball Algorithm provides a streamlined and efficient approach for computing the square root matrix function. The approach demonstrates its effectiveness through numerical experiments on various matrices, showing its superior performance compared to existing state-of-the-art methods. Numerical results show that the restarted Heavy Ball algorithm is feasible and effective for calculating the square root function.

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Invariants Preserving Time-Implicit Local Discontinuous Galerkin Schemes for High-Order Nonlinear Wave Equations

Zheng,

2024

Commun. Appl. Math. Comput.

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A least squares approach for saddle point problems

Cited by 4 publications

References 11 publications

Polynomial-Based Approach for Efficient Function Computation of Symmetric Matrices Using Restarted Heavy Ball Method

Polynomial-Based Approach for Efficient Function Computation of Symmetric Matrices Using Restarted Heavy Ball Method

Streamlining Square Root Matrix Function Computation with Restarted Heavy Ball Algorithm

Invariants Preserving Time-Implicit Local Discontinuous Galerkin Schemes for High-Order Nonlinear Wave Equations

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