scispace - formally typeset
Search or ask a question

Is matrix math hard? 

Singular value decomposition
Matrix decomposition
Computation
Matrix (mathematics)
Iterative method

Answers from top 9 papers

More filters
Papers (9)Insight
Journal Article•DOI
Proximity effect and magnetic field calculation in GIL and in isolated phase bus ducts
Roberto Benato, Fabrizio Dughiero, Michele Forzan, A. Paolucci 
07 Aug 2002-IEEE Transactions on Magnetics
69 Citations
The simplicity of the approach, the conciseness of the matrix algebra applied, and the close-to-reality procedure make this method extremely attractive for self-made software implementation on any commercially available math packages such as Matlab.
Proceedings Article•DOI
Divide-and-Conquer Anchoring for Near-Separable Nonnegative Matrix Factorization and Completion in High Dimensions
Tianyi Zhou, Wei Bian, Dacheng Tao 
01 Dec 2013
26 Citations
A rigorous analysis proves that DCA is able to find the correct anchors of a rank-k matrix by solving math cal O(klog k) sub-problems.
Journal Article•DOI
An iterative method for calculating hard-wall diffraction intensities
Robert H. Swendsen, Karl-Heinz Rieder 
01 Feb 1982-Surface Science
15 Citations
We present here a new iterative method, based on the hard-wall approximation, which has the advantages of programming simplicity, accuracy, and the avoidance of matrix inversions.
Journal Article•DOI
Node and mesh analysis by inspection
J.G. Gottling
01 Nov 1995-IEEE Transactions on Education
14 Citations
Matrix methods of circuit analysis are now appropriate for student use because of the existence of calculators capable of solving large matrices and the availability of inexpensive math programs for personal computers.
Journal Article•DOI
A Low Complexity Signal Detection Scheme Based on Improved Newton Iteration for Massive MIMO Systems
Fangli Jin, Qiufeng Liu, Hao Liu, Peng Wu 
11 Feb 2019-IEEE Communications Letters
33 Citations
And by converting the matrix-matrix product into the matrix-vector product, the computational complexity is substantially reduced.
Journal Article•DOI
Feature extraction and denoising using kernel PCA
A. M. Jade, B. Srikanth, V. K. Jayaraman, Bhaskar D. Kulkarni, Jyoti P. Jog, L. Priya 
01 Oct 2003-Chemical Engineering Science
85 Citations
Use of simple matrix algebra in simulations makes the method an attractive alternative to some hard optimization based methodologies.
Open access•Journal Article•DOI
An iterative test for H -matrix
Toshiyuki Kohno, Hiroshi Niki, Hideo Sawami, Yi-Ming Gao 
01 Mar 2000-Journal of Computational and Applied Mathematics
27 Citations
This method is useful when matrix A is an H -matrix, and when A is not an H -matrix, a wasteful computation is necessary.
Open access•Journal Article•DOI
An algorithm to improve nearly orthonormal sets of vectors on a vector processor
Bernard Philippe
01 Jul 1987-Siam Journal on Algebraic and Discrete Methods
25 Citations
It is especially efficient when the original matrix is near an orthonormal matrix.
Proceedings Article•DOI
Kalman filter algorithm based on singular value decomposition
Liang Wang, Gaetan Libert, Pierre Manneback 
16 Dec 1992
41 Citations
Since the algorithm is formulated in the form of vector-matrix and matrix-matrix operations, it is also useful for parallel computers.

Related Questions

Is there difficult math involved typically?2 answersMathematics is generally considered a difficult subject. Students often face difficulties in learning mathematics, which can be attributed to various factors such as teaching techniques, inadequate school facilities, family environment, and curriculum. However, it is important to note that not all students find math difficult. Some students may excel in mathematics while others may struggle. Difficulties in mathematics can vary depending on the specific topic or concept being taught. For example, students may face difficulties in algebraic operations, such as understanding variables and constants, applying principles of addition and multiplication, and solving algebraic problems. Overall, while mathematics can be challenging for some students, it is not universally difficult and individual experiences may vary.
Did the movie Matrix win any awards?4 answers
Has Matrix won an Oscar?6 answers
How do you do matrix algebra on TI 84?6 answers
Is matrix algebra easy?6 answers
What level of math is matrix algebra?7 answers

See what other people are reading

Is MD2 a monomer or dimer?
5 answers
MD-2, a protein essential for Toll-like receptor 4 (TLR4) activation by lipopolysaccharide (LPS), exists as a mixture of disulfide-linked oligomers, indicating its dimeric nature. The Rho GTPase binding domain of Plexin-B1 (RBD) also exhibits dimerization, affecting its dynamic structure and conformational entropy. In contrast, the monomer-dimer (MD) problem on a random planar honeycomb lattice model involves calculating the MD partition function for bipartite graphs, corresponding to the permanent of a matrix, indicating a dimeric state. Additionally, the study on Mdm2 and MdmX proteins highlights the significance of dimerization for their E3 ubiquitin ligase activity, with mutations affecting dimer formation and subsequent protein degradation, emphasizing the role of dimerization in their functions. Collectively, these findings suggest that MD-2 can exist as a dimeric protein.How does the choice of clustering algorithm impact the accuracy of the OD matrix in trip analysis?
10 answers
The choice of clustering algorithm significantly impacts the accuracy of the Origin-Destination (OD) matrix in trip analysis by affecting the identification of travel patterns, the scalability of route choice models, and the efficiency of OD estimation methods. Clustering algorithms, by grouping similar data points, help in simplifying the complex, high-dimensional OD matrices into more manageable sub-groups, which can be crucial for accurately capturing and analyzing trip patterns. For instance, the use of geographical window-based structural similarity index (GSSI) as a structural proximity measure in the DBSCAN algorithm has shown effectiveness in clustering high-dimensional OD matrices. This approach addresses the challenge of multi-density data points by proposing clustering on individual subspaces, which aids in identifying typical travel patterns and estimating corresponding OD matrices. Similarly, the application of clustering analysis to obtain a small set of representative OD pairs and routes has been demonstrated to improve the predictive accuracy of route choice models, by scaling up observations on traveler behavior from these representative sets to the entire network. Moreover, the integration of clustering methods in the optimization process, as seen in the sensitivity-based OD estimation (SBODE) using the Levenberg-Marquardt (LM) algorithm, leverages information from the Jacobian matrix to define clusters of OD-demand variables. This approach not only enhances the efficiency and efficacy of the algorithm but also reduces the risk of being trapped in local optima by breaking the OD estimation problem into smaller, more manageable sub-problems. In summary, the choice of clustering algorithm plays a pivotal role in enhancing the accuracy of OD matrices by facilitating the identification of distinct travel patterns, enabling scalable and adaptable route choice modeling, and improving the methodological and computational efficiency of OD estimation processes. This underscores the importance of selecting appropriate clustering algorithms tailored to the specific characteristics and challenges of the OD matrix data being analyzed.What is the current state of research on functional connectivity the field of neuroscience?
5 answers
Current research in neuroscience emphasizes the study of functional connectivity to understand brain dynamics and pathologies. Studies employ various methodologies, such as latent factor models for neuronal ensemble interactions, deep learning frameworks for EEG data analysis in schizophrenia patients, and online functional connectivity estimation using EEG/MEG data. These approaches enable real-time tracking of brain activity changes, differentiation of mental states, and prediction of brain disorders with high accuracy. The field's advancements shed light on how neuronal activities are influenced by external cues, brain regions, and cognitive tasks, providing valuable insights into brain function and pathology. Overall, the current state of research showcases a multidimensional exploration of functional connectivity to unravel the complexities of the brain's functional and structural aspects.What are the most common physical characteristics of suspects in criminal investigations?
10 answers
In criminal investigations, the identification and analysis of suspects' physical characteristics are crucial for narrowing down suspects and solving cases. Recent research has highlighted various physical characteristics that are commonly analyzed. Gestures, including hand movements and body language, are significant indicators of a suspect's behavior and can be automatically identified using deep learning techniques with high accuracy levels. Beyond gestures, the anatomical features on the dorsal surface of the hand, such as the occurrence rate of specific hand features, have been studied to assist in forensic investigations, showing significant variation between males and females. DNA analysis has become routine in forensic science, providing not only the genetic profile but also the potential to estimate the biological age of the individual from biological stains, adding another layer of physical characteristic useful in investigations. The ICM_Apriori algorithm has improved the efficiency of mining criminal data, including suspects' characteristics, by significantly reducing the time required for analysis. Interviews and the study of white-collar crime also reveal that socioeconomic status and occupational roles can be considered indirect physical or demographic characteristics relevant in certain criminal investigations. Dermatological conditions affecting fingerprints can complicate the identification process, indicating the importance of skin conditions as a physical characteristic in criminalistics. Facial attributes, defined and extracted using automated algorithms, serve as critical identifiers in the absence of traditional eyewitness sketches, highlighting the role of describable facial features in suspect identification. The personality and lifestyle choices, including substance abuse, can indirectly influence physical characteristics or the perception thereof in criminal profiles. Forensic dentistry emphasizes the uniqueness of dental structures as a vital physical characteristic in identifying suspects or victims in crimes. Lastly, the use of subjective feature-based mug shot retrieval systems demonstrates the importance of witnesses' perceptions of suspects' physical features, further underscoring the variety of characteristics used in criminal investigations.What are the most common characteristics of suspects in criminal investigations?
10 answers
The most common characteristics of suspects in criminal investigations can be discerned through various analytical lenses, including behavioral evidence analysis, psychological profiling, interrogation outcomes, and the application of technology and algorithms in criminal investigations. Behavioral evidence analysis suggests that investigatively relevant characteristics of suspects include criminal skill, knowledge of the victim, the crime scene, and methods and materials, although profilers often err in deducing characteristics like age, sex, and intelligence. The application of technology, specifically deep learning techniques, has shown efficacy in identifying suspects based on unique behavioral cues such as body language and hand gestures, with a high accuracy level in distinguishing between positive and negative gestures. Psychological profiling, particularly through polygraph surveys, highlights the importance of emotional and behavioral traits such as reactive aggression, emotional lability, and a tendency towards emotional instability among suspects. This is complemented by the use of the Behavior Analysis Interview (BAI), which effectively differentiates between deceptive and truthful suspects by assessing verbal and nonverbal cues, with a notable accuracy in identifying deceptive behaviors. Criminal investigations also benefit from the analysis of suspects' characteristics through algorithms like the ICM_Apriori, which improves the efficiency of mining criminal rules and clues from crime data. Moreover, the study of criminal careers reveals patterns of generalist and specialist behaviors among suspects, influenced by factors such as age and gender, with women showing a propensity towards certain types of crimes like fraud. Interrogation outcomes further elucidate suspects' characteristics, indicating that previous contact with the police and personal traits significantly influence the truthfulness and content of suspects' confessions. Additionally, psychological assessments of detainees have identified mental health, memory and suggestibility, previous criminality, and literacy and IQ as significant factors. In summary, the most common characteristics of suspects in criminal investigations encompass a broad spectrum of behavioral, emotional, psychological, and demographic traits, as well as criminal skills and knowledge, all of which are crucial for effective profiling, interrogation, and investigation processes.What are the strategies for re-observation?
5 answers
Re-observation strategies play a crucial role in optimizing the accuracy of re-entry predictions for space debris on high elliptical orbits. Traditional methods relying on Two Line Elements (TLEs) lack precision due to low accuracies and the absence of uncertainty information. To enhance re-entry estimates, utilizing observational data from Earth sensors is beneficial, albeit introducing complexities in designing observation campaigns. Evolutionary algorithms offer a method for optimizing observation strategies, as demonstrated through examples comparing re-entry predictions from TLE data with those from ideal sensor architectures. In a different context, strategies enforcing linear payoff relationships in repeated games, considering discount factors and observation errors, were analyzed. This study identified two types of strategies, including Zero-determinant (ZD) strategies, which manipulate opponents' payoffs irrespective of their strategies, contributing to a deeper understanding of such strategies in society.What are some efficient computational methods that can be used to address scalability challenges in AI algorithms?
5 answers
Efficient computational methods to address scalability challenges in AI algorithms include secure multiparty computation (SMC), quasi-homomorphic encryption, federated learning (FL), and Graph Equilibrium Models (GEQs). While SMC and FL focus on secure distributed processing and data privacy, GEQs tackle long-range dependency issues in graph neural networks. To enhance scalability, a method called VEQ has been proposed, which optimizes the equilibrium finding process by utilizing virtual equilibrium and mini-batch training. These methods aim to balance computational complexity, confidentiality, and performance in large-scale AI applications, offering solutions to the challenges posed by the increasing size and complexity of modern AI algorithms.Can artificial neural networks improve quality control over details and perceptible contexts in various industries?
5 answers
Artificial neural networks (ANNs) have shown promise in enhancing quality control across diverse industries. ANNs, particularly convolutional neural networks, excel in image classification tasks, aiding in quality assessment of food packaging. Research also focuses on optimizing ANN training methodologies for improved performance in solving complex problems like scheduling in transport. In manufacturing, ANNs can help detect defects in automotive parts, preventing the production of faulty batches. Moreover, the emergence of edge computing allows for AI services like feature hierarchical edge inference to control AI quality based on communication and computation loads, catering to diverse user demands. Overall, ANNs offer a versatile tool for enhancing quality control by analyzing details and perceptible contexts in various industries.What is ASCII file?
5 answers
An ASCII file is a type of file format that utilizes ASCII (American Standard Code for Information Interchange) characters for encoding data. ASCII art, a form of ASCII file, represents images using character shapes and is commonly used on internet bulletin boards. ASCII-based encryption/decryption applications can be applied to various file types, such as images, data files, audio files, and more, by translating ASCII values of characters into binary mode. Additionally, an ASCII file format has been proposed for exchanging large systems of nonlinear ordinary differential matrix equations, supporting dense and sparse matrices with the inclusion of nonlinear functions and couplings. Furthermore, ASCII text-cover centric data hiding schemes are being researched to enhance information security through steganography, addressing issues like copyright infringement and e-theft.How does CDOM absorption compare with other methods for predicting water pollution, in terms of accuracy and efficiency?
10 answers
The comparison of CDOM absorption methods with other techniques for predicting water pollution reveals a nuanced landscape of accuracy and efficiency across various studies. CDOM, or chromophoric dissolved organic matter, plays a crucial role in the biogeochemical and carbon cycles of aquatic environments, with its absorption being a significant part of light absorptions in these systems. The use of machine learning algorithms, such as Gaussian process regression (GPR), has shown high stability and estimation accuracy for CDOM absorption coefficients, outperforming traditional empirical models in inland waters. This suggests a potential for high accuracy in CDOM-based monitoring approaches. In contrast, other predictive models for water quality, such as those targeting chemical oxygen demand (COD) using spectral technology and particle swarm algorithms, have also demonstrated good prediction effects. These methods, while distinct from CDOM absorption techniques, offer a stable, fast, and real-time measurement capability that is crucial for effective water pollution control and treatment. UV-visible imaging spectroscopy, an emerging technology, has been anticipated to improve the remote sensing of coastal waters by facilitating the detection of CDOM in optically complex waters. This method, especially when incorporating UV reflectance, significantly improves the retrieval of CDOM absorption coefficients, indicating its efficiency and accuracy in monitoring coastal water quality. Furthermore, the exploration of CDOM sources and dynamics through machine learning models like XGBoost has provided insights into the spectral slopes of CDOM, offering a more detailed understanding of its characteristics in marine environments. The identification of fluorescent components of CDOM in urban waters and their correlation with pollution levels further underscores the utility of CDOM analysis in real-time water quality monitoring. Comparatively, studies on the spectral characteristics of CDOM in highly polluted waters have highlighted the importance of understanding CDOM optical properties and their relationship with water quality. Seasonal characteristics of fluorescent CDOM components in polluted watershed tributaries have also been examined, demonstrating the influence of environmental factors on CDOM dynamics. In summary, while CDOM absorption methods offer promising accuracy and efficiency in monitoring water pollution, especially when enhanced by machine learning algorithms and UV-visible imaging spectroscopy, they are part of a broader toolkit that includes other predictive models for water quality assessment. Each method has its strengths and applications, suggesting that a comprehensive approach, possibly integrating multiple techniques, could provide the most accurate and efficient water pollution prediction.What are the limitations and challenges associated with using CDOM absorption for predicting water pollution?
10 answers
The use of Chromophoric Dissolved Organic Matter (CDOM) absorption as a predictor for water pollution faces several limitations and challenges, as highlighted by recent research. One primary challenge is the difficulty in accurately measuring in situ CDOM absorption coefficients due to the necessity of prefiltration of water samples, which can be cumbersome and time-consuming. Additionally, the complex optical conditions in inland waters, such as those found in eutrophic lakes, can significantly challenge the remote sensing estimates of CDOM, thereby affecting the accuracy of water pollution predictions. Moreover, the spectral characteristics of CDOM can vary significantly with the water quality and spectral parameters, especially in highly polluted waters, making it difficult to develop universally applicable bio-optical models. The variability in CDOM properties across different regions and trophic states further complicates the use of CDOM absorption for predicting water pollution, as the relationship between CDOM and dissolved organic carbon (DOC) can vary, affecting the applicability of remote sensing monitoring. The seasonal characteristics of CDOM also introduce variability, with different fluorescent CDOM components showing seasonal variations that can influence the quantity and quality of CDOM in water samples. This seasonal variability, along with the spatial discrepancy in CDOM optical properties, necessitates the development of region-specific algorithms and models. Furthermore, the emerging technology of UV-visible imaging spectroscopy, while promising for improving the remote sensing of CDOM in optically complex waters, has yet to be fully evaluated for its potential advantages in monitoring CDOM-related water quality. The fluorescence characteristics of CDOM, which can be indicative of pollution levels, also vary spatially and with pollution levels, requiring sophisticated analysis methods like EEM-PARAFAC to interpret. Lastly, the influence of anthropogenic disturbances on CDOM characteristics, as observed in the Liaohe River Delta, underscores the need for tools that can trace the sources and characteristics of CDOM to effectively monitor riverine water quality. These challenges highlight the need for continued research and development of more robust, efficient, and region-specific methods for using CDOM absorption as a predictor for water pollution.