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ITHEA Classification Structure > G. Mathematics of Computing  > G.1 NUMERICAL ANALYSIS  > G.1.6 Optimization 
ITHEA Classification Structure > G. Mathematics of Computing  > G.2 DISCRETE MATHEMATICS  > G.2.m Miscellaneous 
ITHEA Classification Structure > G. Mathematics of Computing  > G.3 PROBABILITY AND STATISTICS 
ЕВКЛИДОВЫ ПРОСТРАНСТВА ЧИСЛОВЫХ ВЕКТОРОВ И
By: Владимир Донченко (4799 reads)
Rating: (1.00/10)

Аннотация: Определены и рассмотрены базовые линейные структуры матричных евклидовых пространств, которые естественным образом расширяют возможности представления моделируемого объекта до «матрицы признаков» и позволяют непосредственным образом учесть динамику исследуемого объекта. «Базовость» структур: линейных и нелинейных, для матричного случая, как и для евклидовых пространств числовых векторов, означает их принципиальное значение для использования в прикладных задачах. Как и в векторном случае, фундаментальную роль в конструктивном построении матричных базовых структур: их описания, взаимного перехода и использования, является аппарат сингулярного представления для линейных операторов между евклидовыми пространствами. Ту же роль в матричном случае сохраняет и псевдообращение по Муру - Пенроузу для линейных операторов на матричных аргументах. В работе представлены результаты, касающиеся сингулярного разложения и псевдообращения по Муру-Пенроузу для матрицы линейных операторов между матричными евклидовыми пространствами. Введены в рассмотрение кортежные объекты и операции над ними, обобщающие понятия классических числовых векторов и блочных матриц ленточного характера. Развита теория группирующих операторов, важная в прикладном отношении как инструмент выявления и использования групповых свойств объектов в евклидовых пространствах, как для пространств числовых векторов, так и для матричных евклидовых пространств. Кроме того, группирующие операторы позволяют, в частности, прояснить алгебраическую суть расстояния Махаланобиса.

Ключевые слова: Псевдообращение по Муру - Пенроузу, сингулярное представление матрицы, кластеризация, расстояние Махаланобиса.

ACM Classification Keywords: G.3 Probability and statistics, G.1.6. Numerical analysis: Optimization; G.2.m. Discrete mathematics: miscellaneous.

Link:

ЕВКЛИДОВЫ ПРОСТРАНСТВА ЧИСЛОВЫХ ВЕКТОРОВ И МАТРИЦ: КОНСТРУКТИВНЫЕ МЕТОДЫ ОПИСАНИЯ БАЗОВЫХ СТРУКТУР И ИХ ИСПОЛЬЗОВАНИЕ

Владимир Донченко

http://foibg.com/ijitk/ijitk-vol05/ijitk05-3-p01.pdf

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G.1.6 Optimization
article: CONSTRUCTING AN OPTIMAL INVESTMENT PORTFOLIO BY USING FUZZY SETS THEORY · FEATURES OF PLANNING TECHNOLOGIES IN COMPUTER-AIDED MANAGEMENT SYSTEMS ... · METHOD FOR CONTROLLING STATE CHANNEL WIRELESS NETWORKS UNDER A PRIORI ... · DIRECT AND DUAL PROBLEM OF INVESTMENT PORTFOLIO OPTIMIZATION UNDER UNCERTAINTY · MATRIXES LEAST SQUARES METHOD AND EXAMPLES OF ITS APPLICATION · КОМПЛЕКСНЫЙ АНАЛИЗ РИСКА БАНКРОТСТВА КОРПОРАЦИЙ В УСЛОВИЯХ НЕОПРЕДЕЛЕННОСТИ · CONSTRUCTING AN OPTIMAL INVESTMENT PORTFOLIO BY USING FUZZY SETS THEORY · A COMPARISON OF SOME APPROACHES TO THE RECOGNITION PROBLEMS IN CASE OF TWO ... · Automated Building Extraction System Applied On High Resolution Satellite ... · SPREADING THE MOORE - PENROSE PSEUDO INVERSE ON MATRICES EUCLIDEAN SPACES: ... · Solution Algorithm of Multicriteria Problems of Lexicographic Optimization ... · ABOUT CRITERIA FOR AN ESTIMATION OF NONLINEAR PARAMETERS IN MODELS OF ... · MATRIX “FEATURE VECTORS” IN GROUPING INFORMATION PROBLEM: LINEAR ... · VECTORS AND MATRIXES LEAST SQUARES METHOD: FOUNDATION AND APPLICATION ... · NUMERICAL INTEGRATION BY GENETIC ALGORITHMS · VECTORS AND MATRIXES IN GROUPING INFORMATION PROBLEM · NON SMOOTH OPTIMIZATION METHODS IN THE PROBLEMS OF CONSTRUCTING A LINEAR ... · RECURRENT PROCEDURE IN SOLVING THE GROUPING INFORMATION PROBLEM IN APPLIED... · АЛГОРИТМ ПОСТРОЕНИЯ ВЫПУКЛОГО ПРОДОЛЖЕНИЯ · ‘FEATURE VECTORS’ IN GROUPING INFORMATION PROBLEM IN APPLIED MATHEMATICS: .. · EFFECTIVE ENERGY RECOMPUTATION FOR LOW AUTOCORRELATION BINARY SEQUENCE PROBLEM · FUZZY SETS AS A MEAN FOR UNCERTAINTY HANDLING: MATH, APPLIED MATH, HEURISTICS · FUZZY SETS: MATH, APPLIED MATH, HEURISTICS? PROBLEMS AND INTERPRETATIONS · ИССЛЕДОВАНИЕ МНОГОКРИТЕРИАЛЬНОЙ ЗАДАЧИ ОП� · РАСПОЗНАВАНИЕ ЗДАНИЙ НА СПУТНИКОВЫХ СНИМКА · ПОСТРОЕНИЕ НЕЛИНЕЙНЫХ КЛАССИФИКАТОРОВ В СЛ · ЕВКЛИДОВЫ ПРОСТРАНСТВА ЧИСЛОВЫХ ВЕКТОРОВ И · TWO APPROACHES TO ONE OPTIMIZATION PROBLEM IN RECOGNITION THEORY · DIFFERENTIAL EVOLUTION – PARTICLE SWARM OPTIMIZATION · EXACT DISCRIMINANT FUNCTION DESIGN USING SOME OPTIMIZATION TECHNIQUES · IMPLEMENTATION OF GENETIC ALGORITHMS FOR TRANSIT POINTS ARRANGEMENT · APPLICATION OF DISCRETE OPTIMIZATION IN SOLVING A PROBLEM OF MULTI-ITEM ... · OPTIMAL DESIGN OF INTELLIGENT CONTROL SYSTEMS OF STEAM TURBINE USING GENETIC ... · OPTIMAL SYNTHESIS OF INTELLIGENT CONTROL SYSTEMS OF ATOMIC POWER STATION USING G · APPLICATION OF GENETIC ALGORITHMS TO VECTOR OPTIMIZATION OF THE AUTOMATIC CONTRO · REFERENCE-NEIGHBOURHOOD SCALARIZATION FOR MULTIOBJECTIVE INTEGER LINEAR ... · MINIMIZATION OF EMPIRICAL RISK IN LINEAR CLASSIFIER PROBLEM · BENCHMARK OF PSO-DE USING BBOB 2010 · PROTEIN STRUCTURE PREDICTION ON A THREE-DIMENSIONAL TRIANGULAR LATTICE · CLASSIFICATION OF HEURISTIC METHODS IN COMBINATORIAL OPTIMIZATION · APPLIED ASPECTS OF MATHEMATICAL MODELING AND OPTIMIZATION ... · DISTRIBUTED GENETIC ALGORITHM IMPLEMENTATION BY MEANS OF REMOTE METHODS ... · APPLICATION OF GENETIC ALGORITHMS TO VECTOR OPTIMIZATION ... · OPTIMAL SYNTHESIS OF INTELLIGENT CONTROL SYSTEMS OF ATOMIC POWER ... · OPTIMAL DESIGN OF INTELLIGENT CONTROL SYSTEMS OF STEAM TURBINE ... · FINDING THE RELATIONSHIP BETWEEN A SEARCH ALGORITHM AND ... · DATA FLOW ANALYSIS AND THE LINEAR PROGRAMMING MODEL1 · REPRESENTATION OF NEURAL NETWORKS BY DYNAMICAL SYSTEMS ·
G.2.m Miscellaneous
article: SPREADING THE MOORE - PENROSE PSEUDO INVERSE ON MATRICES EUCLIDEAN SPACES: ... · MATRIX “FEATURE VECTORS” IN GROUPING INFORMATION PROBLEM: LINEAR ... · VECTORS AND MATRIXES IN GROUPING INFORMATION PROBLEM · RECURRENT PROCEDURE IN SOLVING THE GROUPING INFORMATION PROBLEM IN APPLIED... · ‘FEATURE VECTORS’ IN GROUPING INFORMATION PROBLEM IN APPLIED MATHEMATICS: .. · FUZZY SETS AS A MEAN FOR UNCERTAINTY HANDLING: MATH, APPLIED MATH, HEURISTICS · FUZZY SETS: MATH, APPLIED MATH, HEURISTICS? PROBLEMS AND INTERPRETATIONS · ЕВКЛИДОВЫ ПРОСТРАНСТВА ЧИСЛОВЫХ ВЕКТОРОВ И ·
G.3 PROBABILITY AND STATISTICS
article: DECISION-MAKING IN GROUPS OF INTERVAL ALTERNATIVES · RISK BEHAVIOUR IN A SET OF INTERVAL ALTERNATIVES · Peculiarities Analysis of Statistical Information in ICT · About convergence of fuzzy perceptive elements sequences, defined on ... · INFORMATION SYSTEM OF FORECASTING BASED ON COMBINED MODELS WITH TIME SERIES ... · Integrated Approach to the Study of Fractal Time Series · METHOD OF DATA ANALYSIS BASED ON CLUSTERING IN “SYNDROMES” INDICATORS SPACE · MATRIXES LEAST SQUARES METHOD AND EXAMPLES OF ITS APPLICATION · PHYSICAL PHENOMENON OF STATISTICAL STABILITY · ANALYSIS OF FEATURES AND POSSIBILITIES OF BANK FUNCTIONING EFFICIENCY BASED ... · SUB-OPTIMAL NONPARAMETRIC HYPOTHESES DISCRIMINATING WITH GUARANTEED DECISION · Solution of the Problem of Formal Evaluation of Effectiveness of ... · ANALYSIS OF THE PROPERTIES OF ORDINARY LEVY MOTION BASED ON THE ESTIMATION ... · SPREADING THE MOORE - PENROSE PSEUDO INVERSE ON MATRICES EUCLIDEAN SPACES: ... · Evaluating Expected Effectiveness of Interval Alternatives · · EVALUATING EXPECTED EFFECTIVENESS OF INTERVAL ALTERNATIVES · COMPARISON OF DIFFERENT WAVELET BASES IN THE CASE OF WAVELETS EXPANSIONS... · О ПРИМЕНИМОСТИ ОЦЕНКО МАТЕМАТИЧЕСКОГО ОЖИД · VECTORS AND MATRIXES LEAST SQUARES METHOD: FOUNDATION AND APPLICATION ... · VECTORS AND MATRIXES IN GROUPING INFORMATION PROBLEM · ОЦЕНКА ИНТЕРВАЛЬНЫХ АЛЬТЕРНАТИВ:... · ON SOME PROPERTIES OF REGRESSION MODELS BASED ON CORRELATION MAXIMIZATION ... · RECURRENT PROCEDURE IN SOLVING THE GROUPING INFORMATION PROBLEM IN APPLIED... · DIVERGENT AND MULTIPLE-VALUED SEQUENCES AND FUNCTIONS · ‘FEATURE VECTORS’ IN GROUPING INFORMATION PROBLEM IN APPLIED MATHEMATICS: .. · MODELING TELECOMMUNICATIONS TRAFFIC USING THE STOCHASTIC MULTIFRACTAL CASCADE... · INTERVALS AS ULTRAMETRIC APPROXIMATIONS ACCORDING TO THE SUPREMUM NORM · DIFFERENTIAL GEOMETRY DERIVED FROM DIVERGENCE FUNCTIONS... · COMPARATIVE ANALYSIS FOR ESTIMATING OF THE HURST EXPONET FOR STATIONARY AND ... · DISTURBANCE OF STATISTICAL STABILITY (PART II) · FUZZY SETS AS A MEAN FOR UNCERTAINTY HANDLING: MATH, APPLIED MATH, HEURISTICS · FUZZY SETS: MATH, APPLIED MATH, HEURISTICS? PROBLEMS AND INTERPRETATIONS · СИММЕТРИЯ В ЗАПИСИ ГЕНЕТИЧЕСКОЙ ИНФОРМАЦИИ · ЕВКЛИДОВЫ ПРОСТРАНСТВА ЧИСЛОВЫХ ВЕКТОРОВ И · METHOD FOR EVALUATING OF DISCREPANCY BETWEEN REGULARITIES SYSTEMS IN ... · CORRELATION MAXIMIZATION IN REGRESSION MODELS BASED ON CONVEX COMBINATIONS · NEURAL NETWORK SEGMENTATION OF VIDEO VIA TIME SERIES ANALYSIS · GOD-ICS. ON FUNDAMENTAL INFORMATION FIELD QUEST · ОЦЕНИВАНИЕ РИСКА РЕГРЕССИОННОЙ МОДЕЛИ В СЛ� · ПОСТРОЕНИЕ ЛОГИКО-ВЕРОЯТНОСТНЫХ МОДЕЛЕЙ В� · ОПТИМИЗАЦИЯ ОЦЕНКИ ВЕРОЯТНОСТИ ОШИБОЧНОЙ К · ON A PROBLEM OF QOS CHARACTERISTICS INTERPRETATION IN TRANSIT NETWORKS · OPTIMAL FORECASTING BASED ON CONVEXCORRECTING PROCEDURES · COMPARATIVE ANALYSIS OF STATISTICAL PROPERTIES OF THE HURST EXPONENT ... · DISTURBANCE OF STATISTICAL STABILITY · A SURVEY OF NONPARAMETRIC TESTS FOR THE STATISTICAL ANALYSIS OF EVOLUTIONARY ... · COGNITION HORIZON AND THE THEORY OF HYPER-RANDOM PHENOMENA · IMPROVED CRYPTOANALYSIS OF THE SELF-SHRINKING ... · EVALUATION OF PARETO/D/1/K QUEUE BY SIMULATION · N A PROBLEM OF QOS CHARACTERISTICS INTERPRETATION IN TRANSIT NETWORKS · APPLICATION OF THE HETEROGENEOUS SYSTEM PREDICTION METHOD · STUDY OF QUEUEING BEHAVIOUR IN IP BUFFERS · EXTREME SITUATIONS PREDICTION BY MULTIDIMENSIONAL HETEROGENEOUS ... · APPLICATION OF THE MULTIVARIATE PREDICTION METHOD TO TIME SERIES 1 · DETECTION OF LOGICAL-AND-PROBABILISTIC CORRELATION IN TIME SERIES1 ·
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