• Title, Summary, Keyword: factorization

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Factorization Problem Solving and Analogy (인수분해 문제 해결과 유추)

  • 이종희;김선희
    • School Mathematics
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    • v.4 no.4
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    • pp.581-599
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    • 2002
  • This study investigated the factorization concept development level of 3rd grades in middle school, the success of factorization problem solving, and the completion of factorization analogy tasks and science concepts analogy tasks. This study's results are followings. 1. Based on Sfard' reification levels, we classified students' factorization concept development levels from level 0 to level 3. As the students' development level was high, they tended to succeed the factorization problems gradually. 2. Experiencing factorization tasks which made students arrange factorization expressions hating same characterization, students ' factorization problem solving was improved. And, as the students' development level was high, they tended to attend to internal structural relations in factorization analogy tasks. 3. Analogy in factorization wasn't interrelated with analogy in science concepts. It said that analogy depended on the knowledges with it.

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Study of Spectral Factorization using Circulant Matrix Factorization to Design the FIR/IIR Lattice Filters (FIR/IIR Lattice 필터의 설계를 위한 Circulant Matrix Factorization을 사용한 Spectral Factorization에 관한 연구)

  • 김상태;박종원
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.7 no.3
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    • pp.437-447
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    • 2003
  • We propose the methods to design the finite impulse response (FIR) and the infinite impulse response (IIR) lattice filters using Schur algorithm through the spectral factorization of the covariance matrix by circulant matrix factorization (CMF). Circulant matrix factorization is also very powerful tool used fur spectral factorization of the covariance polynomial in matrix domain to obtain the minimum phase polynomial without the polynomial root finding problem. Schur algorithm is the method for a fast Cholesky factorization of Toeplitz matrix, which easily determines the lattice filter parameters. Examples for the case of the FIR Inter and for the case of the IIR filter are included, and performance of our method check by comparing of our method and another methods (polynomial root finding and cepstral deconvolution).

NON-UNIQUE FACTORIZATION DOMAINS

  • Shin, Yong-Su
    • Journal of applied mathematics & informatics
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    • v.26 no.3_4
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    • pp.779-784
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    • 2008
  • We show that $\mathbb{Z}[\sqrt{-p}]$ is not a unique factorization domain (UFD) but a factorization domain (FD) with a condition $1\;+\;a^2p\;=\;qr$, where a and p are positive integers and q and r are positive primes in $\mathbb{Z}$ with q < p. Using this result, we also construct several specific non-unique factorization domains which are factorization domains. Furthermore, we prove that an integral domain $\mathbb{Z}[\sqrt{-p}]$ is not a UFD but a FD for some positive integer p.

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Compare to Factorization Machines Learning and High-order Factorization Machines Learning for Recommend system (추천시스템에 활용되는 Matrix Factorization 중 FM과 HOFM의 비교)

  • Cho, Seong-Eun
    • Journal of Digital Contents Society
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    • v.19 no.4
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    • pp.731-737
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    • 2018
  • The recommendation system is actively researched for the purpose of suggesting information that users may be interested in in many fields such as contents, online commerce, social network, advertisement system, and the like. However, there are many recommendation systems that propose based on past preference data, and it is difficult to provide users with little or no data in the past. Therefore, interest in higher-order data analysis is increasing and Matrix Factorization is attracting attention. In this paper, we study and propose a comparison and replay of the Factorization Machines Leaning(FM) model which is attracting attention in the recommendation system and High-Order Factorization Machines Learning(HOFM) which is a high - dimensional data analysis.

BLOCK INCOMPLETE FACTORIZATION PRECONDITIONERS FOR A SYMMETRIC H-MATRIX

  • Yun, Jae-Heon;Kim, Sang-Wook
    • Bulletin of the Korean Mathematical Society
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    • v.37 no.3
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    • pp.551-568
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    • 2000
  • We propose new parallelizable block incomplete factorization preconditioners for a symmetric block-tridiagonal H-matrix. Theoretical properties of these block preconditioners are compared with those of block incomplete factorization preconditioners for the corresponding comparison matrix. Numerical results of the preconditioned CG(PCG) method using these block preconditioners are compared with those of PCG method using a standard incomplete factorization preconditioner to see the effectiveness of the block incomplete factorization preconditioners.

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Experimental Study on Supernodal Column Choleksy Factorization in Interior-Point Methods (내부점방법을 위한 초마디 열촐레스키 분해의 실험적 고찰)

  • 설동렬;정호원;박순달
    • Korean Management Science Review
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    • v.15 no.1
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    • pp.87-95
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    • 1998
  • The computational speed of interior point method depends on the speed of Cholesky factorization. The supernodal column Cholesky factorization is a fast method that performs Cholesky factorization of sparse matrices with exploiting computer's characteristics. Three steps are necessary to perform the supernodal column Cholesky factorization : symbolic factorization, creation of the elimination tree, ordering by a post-order of the elimination tree and creation of supernodes. We study performing sequences of these three steps and efficient implementation of them.

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Design of FIR/IIR Lattice Filters using the Circulant Matrix Factorization (Circulant Matrix Factorization을 이용한 FIR/IIR Lattice 필터의 설계)

  • Kim Sang-Tae;Lim Yong-Kon
    • Journal of the Institute of Electronics Engineers of Korea TC
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    • v.41 no.1
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    • pp.35-44
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    • 2004
  • We Propose the methods to design the finite impulse response (FIR) and the infinite impulse response (IIR) lattice filters using Schur algorithm through the spectral factorization of the covariance matrix by circulant matrix factorization (CMF). Circulant matrix factorization is also very powerful tool used for spectral factorization of the covariance polynomial in matrix domain to obtain the minimum phase polynomial without the polynomial root finding problem. Schur algorithm is the method for a fast Cholesky factorization of Toeplitz matrix, which easily determines the lattice filter parameters. Examples for the case of the FIR filter and for the case of the In filter are included, and performance of our method check by comparing of our method and another methods (polynomial root finding and cepstral deconvolution).

유일인수분해에 대하여

  • 최상기
    • Journal for History of Mathematics
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    • v.16 no.3
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    • pp.89-94
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    • 2003
  • Though the concept of unique factorization was formulated in tile 19th century, Euclid already had considered the prime factorization of natural numbers, so called tile fundamental theorem of arithmetic. The unique factorization of algebraic integers was a crucial problem in solving elliptic equations and the Fermat Last Problem in tile 19th century On the other hand the unique factorization of the formal power series ring were a critical problem in the past century. Unique factorization is one of the idealistic condition in computation and prime elements and prime ideals are vital ingredients in thinking and solving problems.

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FACTORIZATION IN MODULES AND SPLITTING MULTIPLICATIVELY CLOSED SUBSETS

  • Nikseresht, Ashkan
    • Journal of the Korean Mathematical Society
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    • v.55 no.1
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    • pp.83-99
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    • 2018
  • We introduce the concept of multiplicatively closed subsets of a commutative ring R which split an R-module M and study factorization properties of elements of M with respect to such a set. Also we demonstrate how one can utilize this concept to investigate factorization properties of R and deduce some Nagata type theorems relating factorization properties of R to those of its localizations, when R is an integral domain.

A FAST FACTORIZATION ALGORITHM FOR A CONFLUENT CAUCHY MATRIX

  • KIM KYUNGSUP
    • Journal of the Korean Mathematical Society
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    • v.42 no.1
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    • pp.1-16
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    • 2005
  • This paper presents a fast factorization algorithm for confluent Cauchy-like matrices. The algorithm consists of two parts. First. a confluent Cauchy-like matrix is transformed into a Cauchy-like matrix available to pivot without changing its structure. Second. a fast partial pivoting factorization algorithm for the Cauchy-like matrix is presented. A new displacement structure cannot possibly generate all entries of a transformed matrix, which is called by 'partially reconstructible'. This paper also discusses how the proposed factorization algorithm can be generally applied to partially reconstructive matrices.