Fast 3D Block Parallelisation for the Matrix Multiplication Prefix Problem

2010 ◽  
pp. 39-50 ◽  
Author(s):  
K. Waldherr ◽  
T. Huckle ◽  
T. Auckenthaler ◽  
U. Sander ◽  
T. Schulte-Herbrüggen
Keyword(s):  
Matrix Multiplication ◽  
The Matrix

scholarly journals PENERAPAN METODE MULTI ATTRIBUTE UTILITY THEORY (MAUT) DALAM PEMETAAN TINGKAT DAMPAK BENCANA BANJIR DI KABUPATEN BANTUL

Telematika ◽  
2020 ◽  
Vol 17 (1) ◽  
pp. 26
Author(s):  
Afif Irfan Abdurrahman ◽  
Bambang Yuwono ◽  
Yuli Fauziah
Keyword(s):  
Utility Theory ◽  
Matrix Multiplication ◽  
Flood Disaster ◽  
Accuracy Rate ◽  
Affected Area ◽  
A Value ◽  
Multi Attribute Utility Theory ◽  
The Matrix ◽  
The Difference ◽  
The Impact

Flood disaster is a dangerous disaster, an event that occurs due to overflow of water resulting in submerged land is called a flood disaster. Almost every year Bantul Regency is affected by floods due to high rainfall. The flood disaster that struck in Bantul Regency made the Bantul District Disaster Management Agency (BPBD) difficult to handle so that it needed a mapping of the level of the impact of the flood disaster to minimize the occurrence of floods and provide information to the public.This study will create a system to map the level of impact of floods in Bantul Regency with a decision support method namely Multi Attribute Utility Theory (MAUT). The MAUT method stage in determining the level of impact of flood disasters through the process of normalization and matrix multiplication. The method helps in determining the areas affected by floods, by managing the Indonesian Disaster Information Data (DIBI). The data managed is data on criteria for the death toll, lost victims, damage to houses, damage to public facilities, and damage to roads. Each criteria data has a value that can be used to determine the level of impact of a flood disaster. The stages for determining the level of impact of a disaster require a weighting calculation process. The results of the weighting process display the scoring value which has a value of 1 = low, 2 = moderate, 3 = high. To assist in determining the affected areas using the matrix normalization and multiplication process the process is the application of the Multi Attribute Utility Theory (MAUT) method.This study resulted in a mapping of the level of impact displayed on google maps. The map view shows the affected area points and the level of impact of the flood disaster in Bantul Regency. The mapping produced from the DIBI data in 2017 produced the highest affected area in the Imogiri sub-district. The results of testing the data can be concluded that the results of this study have an accuracy rate of 95% when compared with the results of the mapping previously carried out by BPBD Bantul Regency. The difference in the level of accuracy is because the criteria data used are not the same as the criteria data used by BPBD in Bantul Regency so that the accuracy rate is 95%.

scholarly journals On Solutions of the Matrix Equation A ∘ l X  = B with respect to M M -2 Semitensor Product

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Jin Wang
Keyword(s):  
Matrix Equation ◽  
Matrix Multiplication ◽  
Sufficient Condition ◽  
Mathematical Tool ◽  
Necessary And Sufficient Condition ◽  
The Matrix ◽  
Necessary And Sufficient

M M -2 semitensor product is a new and very useful mathematical tool, which breaks the limitation of traditional matrix multiplication on the dimension of matrices and has a wide application prospect. This article aims to investigate the solutions of the matrix equation A ° l X = B with respect to M M -2 semitensor product. The case where the solutions of the equation are vectors is discussed first. Compatible conditions of matrices and the necessary and sufficient condition for the solvability is studied successively. Furthermore, concrete methods of solving the equation are provided. Then, the case where the solutions of the equation are matrices is studied in a similar way. Finally, several examples are given to illustrate the efficiency of the results.

scholarly journals An Accelerator Architecture of Changeable-Dimension Matrix Computing Method for SVM

Electronics ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 143 ◽  
Author(s):  
Ruidong Wu ◽  
Bing Liu ◽  
Ping Fu ◽  
Junbao Li ◽  
Shou Feng
Keyword(s):  
Machine Learning ◽  
Learning Algorithms ◽  
Matrix Multiplication ◽  
Critical Time ◽  
Machine Learning Algorithms ◽  
Support Vector ◽  
Practical Applications ◽  
The Matrix ◽  
Field Programmable ◽  
Computing Method

Matrix multiplication is a critical time-consuming processing step in many machine learning applications. Due to the diversity of practical applications, the matrix dimensions are generally not fixed. However, most matrix calculation methods, based on field programmable gate array (FPGA) currently use fixed matrix dimensions, which limit the flexibility of machine learning algorithms in a FPGA. The bottleneck lies in the limited FPGA resources. Therefore, this paper proposes an accelerator architecture for matrix computing method with changeable dimensions. Multi-matrix synchronous calculation concept allows matrix data to be processed continuously, which improves the parallel computing characteristics of FPGA and optimizes the computational efficiency. This paper tests matrix multiplication using support vector machine (SVM) algorithm to verify the performance of proposed architecture on the ZYNQ platform. The experimental results show that, compared to the software processing method, the proposed architecture increases the performance by 21.18 times with 9947 dimensions. The dimension is changeable with a maximum value of 2,097,151, without changing hardware design. This method is also applicable to matrix multiplication processing with other machine learning algorithms.

scholarly journals On a New Formula for Fibonacci’s Family m-step Numbers and Some Applications

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 805 ◽  
Author(s):  
Monther Rashed Alfuraidan ◽  
Ibrahim Nabeel Joudah
Keyword(s):  
Number Theory ◽  
Time Complexity ◽  
Matrix Multiplication ◽  
Square Roots ◽  
Computational Number Theory ◽  
The Matrix ◽  
Theory Application ◽  
Constant Coefficients ◽  
New Formula

In this work, we obtain a new formula for Fibonacci’s family m-step sequences. We use our formula to find the nth term with less time complexity than the matrix multiplication method. Then, we extend our results for all linear homogeneous recurrence m-step relations with constant coefficients by using the last few terms of its corresponding Fibonacci’s family m-step sequence. As a computational number theory application, we develop a method to estimate the square roots.

scholarly journals Semitensor Product Compressive Sensing for Big Data Transmission in Wireless Sensor Networks

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Haipeng Peng ◽  
Ye Tian ◽  
Jürgen Kurths
Keyword(s):  
Big Data ◽  
Compressive Sensing ◽  
Data Transmission ◽  
Matrix Multiplication ◽  
Wireless Sensor ◽  
Storage Space ◽  
Secret Key ◽  
Encrypt Data ◽  
The Matrix ◽  
Data Volume

Big data transmission in wireless sensor network (WSN) consumes energy while the node in WSN is energy-limited, and the data transmitted needs to be encrypted resulting from the ease of being eavesdropped in WSN links. Compressive sensing (CS) can encrypt data and reduce the data volume to solve these two problems. However, the nodes in WSNs are not only energy-limited, but also storage and calculation resource-constrained. The traditional CS uses the measurement matrix as the secret key, which consumes a huge storage space. Moreover, the calculation cost of the traditional CS is large. In this paper, semitensor product compressive sensing (STP-CS) is proposed, which reduces the size of the secret key to save the storage space by breaking through the dimension match restriction of the matrix multiplication and decreases the calculation amount to save the calculation resource. Simulation results show that STP-CS encryption can achieve better performances of saving storage and calculation resources compared with the traditional CS encryption.

MAPPED LEAST SQUARES SUPPORT VECTOR MACHINE REGRESSION

2005 ◽  
Vol 19 (03) ◽  
pp. 459-475 ◽  
Author(s):  
SHENG ZHENG ◽  
YUQIU SUN ◽  
JINWEN TIAN ◽  
JAIN LIU
Keyword(s):  
Least Squares ◽  
Matrix Multiplication ◽  
Learning Problems ◽  
Support Vector ◽  
Training Algorithms ◽  
Learning Problem ◽  
Multiplication Operation ◽  
Vector Machines ◽  
The Matrix ◽  
Set Of Points

This paper describes a novel version of regression SVM (Support Vector Machines) that is based on the least-squares error. We show that the solution of this optimization problem can be obtained easily once the inverse of a certain matrix is computed. This matrix, however, depends only on the input vectors, but not on the labels. Thus, if many learning problems with the same set of input vectors but different sets of labels have to be solved, it makes sense to compute the inverse of the matrix just once and then use it for computing all subsequent models. The computational complexity to train an regression SVM can be reduced to O (N2), just a matrix multiplication operation, and thus probably faster than known SVM training algorithms that have O (N2) work with loops. We describe applications from image processing, where the input points are usually of the form {(x0 + dx, y0 + dy) : |dx| < m, |dy| < n} and all such set of points can be translated to the same set {(dx, dy) : |dx| < m, |dy| < n} by subtracting (x0, y0) from all the vectors. The experimental results demonstrate that the proposed approach is faster than those processing each learning problem separately.

Technology Tips: Exploring Hill Ciphers with Graphing Calculators

1998 ◽  
Vol 91 (3) ◽  
pp. 240-244
Author(s):  
Dennis St. John
Keyword(s):  
Relative Frequency ◽  
English Language ◽  
Matrix Multiplication ◽  
Graphing Calculator ◽  
School Mathematics ◽  
Modular Arithmetic ◽  
Evaluation Standards ◽  
Hill Cipher ◽  
The Matrix ◽  
Coded Messages

Throughout history, coded messages have been used for various reasons. Today's students are fascinated by the secretive nature of these codes, and this fascination can lead them to explore the mathematics of cryptography. The simplest codes are called substitution ciphers. In these codes, each letter is replaced by another number or letter in the alphabet. These codes are easy to crack, or decode, because of the relative frequency of letters in messages. For example, e is the most often used letter in the English language; therefore, the substituted value for e is relatively easy to determine. One way to make substitution codes more difficult to crack is to group letters and then encode the groups of letters. A particular application of this strategy, one that combines matrix multiplication and modular arithmetic, is known as the Hill cipher (Anton and Rorres 1987). This article explains coding and decoding messages using Hill ciphers. These ciphers are an interesting example of an application of matrices called for in NCTM's Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) for grades 9-12. A graphing calculator will facilitate the matrix and modular arithmetic used in the coding and decoding procedures.

scholarly journals PROFIL KESALAHAN SISWA DALAM MENYELESAIKAN SOAL MATRIKS BERDASARKAN JENIS KELAMIN DI SMA NEGERI 7 PALU

Aksioma ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 110-124
Author(s):  
Fausan Fausan ◽  
Gandung Sugita ◽  
Sukayasa Sukayasa
Keyword(s):  
Matrix Multiplication ◽  
Male Student ◽  
Female Students ◽  
Inverse Matrix ◽  
Male Students ◽  
Research Subjects ◽  
Multiplication Formula ◽  
Interview Methods ◽  
The Matrix ◽  
Matrix Problems

Abstrak: Penelitian ini merupakan penelitian kualitatif yang bertujuan untuk memperoleh profil kesalahan yang dilakukan siswa dalam menyelesaikan soal matriks berdasarkan jenis kelamin di SMA Negeri 7 Palu. Data dikumpulkan dengan cara metode tes dan wawancara. Subjek penelitian terdiri dari satu siswa laki-laki (SH) dan satu siswa perempuan (DS). Hasil Penelitian menunjukkan bahwa kesalahan konseptual yang dilakukan siswa laki-laki (SH) yaitu : 1) kesalahan tidak memahami konsep rumus perkalian matriks, 2) kesalahan konsep perkalian matriks, 3) kesalahan tidak menerapkan rumus invers, 4) kesalahan konsep invers matriks dan 5)  kesalahan konsep adjoin. Kesalahan prosedural yang dilakukan siswa laki-laki berupa 1) kesalahan dalam melakukan perhitungan, 2) kesalahan tidak menyederhanakan dan 3) kesalahan tidak menuliskan tanda operasi pada matriks. Sedangkan kesalahan konseptual yang dilakukan siswa perempuan (DS) yaitu: 1) kesalahan tidak memahami konsep rumus perkalian matriks, 2) kesalahan konsep perkalian matriks, 3) kesalahan konsep adjoin dan 4) kesalahan konsep invers matriks. Kesalahan prosedural yang dilakukan siswa perempuan berupa 1) kesalahan dalam melakukan perhitungan. Siswa laki-laki banyak melakukan kesalahan dari pada siswa perempuan dikarenakan, siswa laki-laki tidak teliti dan terburu-buru dalam menyelesaikan soal matriks. Sedangkan siswa perempuan tidak terlalu banyak melakukan kesalahan dikarenakan cenderung lebih teliti dan cermat dalam menyelesaikan soal matriks. Kata kunci: Profil Kesalahan, Jenis Kelamin dan Matriks Abstract: This research is a qualitative research which aims to obtain a profile of errors students make in solving matrix problems based on sex in SMA 7 Palu. Data was collected by means of test and interview methods. The research subjects consisted of one male student (SH) and one female student (DS). The results showed that the conceptual errors made by male students (SH) were: 1) errors not understanding the concept of matrix multiplication formula, 2) errors in matrix multiplication concepts, 3) errors not applying inverse formulas, 4) inverse matrix concept errors and 5 ) the error of the adjoin concept. Procedural errors made by male students in the form of 1) errors in making calculations, 2) errors do not simplify and 3) errors do not write the operation mark on the matrix. Whereas the conceptual errors made by female students (DS) are: 1) errors do not understand the concept of matrix multiplication formula, 2) errors in the concept of matrix multiplication, 3) errors in adjoining concepts and 4) inverse matrix concept errors. Procedural errors made by female students in the form of 1) errors in carrying out calculations. Male students make a lot of mistakes than female students because , male students are not careful and in a hurry to solve the matrix problem. Whereas female students don't make too many mistakes becausethey tend to be more thorough and careful in solving matrix problems. Keywords: Error Profile, Gender and Matrix

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