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			Vol 65, No 3 (2025)
General numerical methods
SIMULTANEOUS DIAGONABILITY OF A PAIR OF MATRICES: SIMILARITY AND CONGRUENCE
Abstract
 245-250
				
					245-250
				
						 
			
				 
				
			
		INDEXING IN THE GOOD–THOMAS FAST FOURIER TRANSFORM ALGORITHM
Abstract
 251-257
				
					251-257
				
						 
			
				 
				
			
		Optimal control
ANTISYMMETRIC EXTREMUM MAPPING AND LINEAR DYNAMICS
Abstract
 258-274
				
					258-274
				
						 
			
				 
				
			
		SPARSE AND TRANSFERABLE UNIVERSAL SINGULAR VECTORS ATTACK
Abstract
Mounting concerns about neural networks’ safety and robustness call for a deeper understanding of models’ vulnerability and research in adversarial attacks. Motivated by this, we propose a novel universal attack that is highly efficient in terms of transferability. In contrast to the existing (p, q)-singular vectors approach, we focus on finding sparse singular vectors of Jacobian matrices of the hidden layers by employing the truncated power iteration method. We discovered that using resulting vectors as adversarial perturbations can effectively attack the original model and models with entirely different architectures, highlighting the importance of sparsity constraint for attack transferability. Moreover, we achieve results comparable to dense baselines while damaging less than 1% of pixels and utilizing only 256 samples for perturbation fitting. Our algorithm also admits higher attack magnitude without affecting the human ability to solve the task, and damaging 5% of pixels attains more than a 50% fooling rate on average across models. Finally, our findings demonstrate the vulnerability of state-of-the-art models to universal sparse attacks and highlight the importance of developing robust machine learning systems.
 275-293
				
					275-293
				
						 
			
				 
				
			
		SUMMATION METHOD FOR FOURIER SERIES ASSOCIATED WITH A MIXED PROBLEM FOR THE INHOMOGENEOUS TELEGRAPH EQUATION
Abstract
 294-300
				
					294-300
				
						 
			
				 
				
			
		APPLICATION OF INTERVAL SLOPES IN NONSMOOTH ONE-DIMENSIONAL OPTIMIZATION PROBLEMS
Abstract
 301-324
				
					301-324
				
						 
			
				 
				
			
		OPTIMAL APPROXIMATION OF AVERAGE REWARD MARKOV DECISION PROCESSES
Abstract
We continue to develop the concept of studying the ε-optimal policy for Average Reward Markov Decision Processes (AMDP) by reducing it to Discounted Markov Decision Processes (DMDP). Existing research often stipulates that the discount factor must not fall below a certain threshold. Typically, this threshold is close to one, and as is well-known, iterative methods used to find the optimal policy for DMDP become less effective as the discount factor approaches this value. Our work distinguishes itself from existing studies by allowing for inaccuracies in solving the empirical Bellman equation. Despite this, we have managed to maintain the sample complexity that aligns with the latest results. We have succeeded in separating the contributions from the inaccuracy of approximating the transition matrix and the residuals in solving the Bellman equation in the upper estimate so that our findings enable us to determine the total complexity of the epsilon-optimal policy analysis for DMDP across any method with a theoretical foundation in iterative complexity. Bybl. 17. Fig. 5. Table 1.
 325-337
				
					325-337
				
						 
			
				 
				
			
		THE NEW IS THE WELL-FORGOTTEN OLD — F4 ALGORITHM OPTIMIZATION
Abstract
 338-346
				
					338-346
				
						 
			
				 
				
			
		Error Analysis of Numerical Methods for Optimization Problems
Abstract
 347-363
				
					347-363
				
						 
			
				 
				
			
		AN ADAPTIVE VARIANT OF THE FRANK–WOLFE METHOD FOR RELATIVE SMOOTH CONVEX OPTIMIZATION PROBLEMS
Abstract
 364-375
				
					364-375
				
						 
			
				 
				
			
		Partial Differential Equations
ON THE UNIQUENESS OF DISCRETE GRAVITY AND MAGNETIC POTENTIALS
Abstract
 376-389
				
					376-389
				
						 
			
				 
				
			
		CAUCHY PROBLEM FOR THE ONE-DIMENSIONAL EQUATION OF MOTION IN A METAMATERIAL
Abstract
 390-400
				
					390-400
				
						 
			
				 
				
			
		Computer science
MATHEMATICAL RECONSTRUCTION OF SIGNALS AND IMAGES USING TEST TRIALS: A NON-BLIND APPROACH
Abstract
 401-414
				
					401-414
				
						 
			
				 
				
			
		 
					 
						 
						 
						 
						 
				



