• The Transactions of the Korea Information Processing Society
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• v.5 no.4
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• pp.959-966
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• 1998

We present fast QR factorization algorithms $m{\times}n\;(m{\geq}n)$ Toeplitz matrix. These QR factorization algortihms are determined from the shift-invariance properties of underlying matrices. The major transformation tool is a stabilized/hyperbolic Householder transformation. The algortihms require O(mn) operations, and can be easily implemented on distributed-memory multiprocessors.

• 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.

• The Mathematical Education
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• v.54 no.4
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• pp.365-383
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• 2015

Factorization asks the recognition of the structure of polynomials, compared to polynomial expansion with process characteristic. Therefore it makes students experience a lot of difficulties. This study aims to figure out causes of the difficulties by identifying students' cognitive characteristics in factorizing in the perspective of 'structure sense'. To do this, we gave six factorizing problems of three types to middle school students and selected six participants as interviewees based on the test results. They were classified into two categories, structure sense and non-structure sense. Through this interview, we figured out the interviewee's cognitive characteristics and the causes of difficulty in the perspective of structure sense. Furthermore, we suggested some didactical implications for encouraging structure sense in factorizing by identifying assistances and obstacles for recognition of structures.

• Proceedings of the Korean Information Science Society Conference
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• 2007.10a
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• pp.209-210
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• 2007

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2006.10a
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• pp.107-107
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• 2006

• Proceedings of the Korean Society of Fisheries Technology Conference
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• 1998.06a
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• pp.175.2-176
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• 1998

• Proceedings of the Korea Information Processing Society Conference
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• 2006.05a
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• pp.469-472
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• 2006

본 논문은 비음수 행렬 인수분해(NMF, non-negative matrix factorization)를 이용하여 문장을 추출하여 문서를 요약하는 새로운 방법을 제안하였다. 제안된 방법은 문장추출에 사용되는 의미 특징(semantic feature)이 비 음수 값을 갖기 때문에 잠재의미분석에 비해 문서의 내용을 정확하게 요약한다. 또한, 적은 계산비용을 통하여 쉽게 요약 문장을 추출할 수 있는 장점을 갖는다.

• Proceedings of the Korean Information Science Society Conference
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• 2006.06a
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• pp.394-396
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• 2006

기존 질의기반의 문서요약은 질의와 문서간의 사전 학습으로 요약의 질을 높이거나, 문서의 고유 구조(inherent structure)를 반영하여 요약의 정확도를 높이기 위하여 문서를 그래프로 변환한다. 본 논문은 비음수 행렬 인수분해 (NMF, Non-negative Matrix Factorization)를 이용하여 질의 기반의 문서를 요약하는 새로운 방법을 제안하였다. 제안된 방법은 질의와 문서간에 사전학습이 필요 없다. 또한 문서를 그래프로 변형시키는 복잡한 처리 없이 NMF에 의해 얻어진 의미 특징(semantic feature)과 의미 변수(semantic variable)로 문서의 고유 구조를 반영하여 요약의 정확도를 높일 수 있다. 마지막으로 단순한 방법으로 문장을 쉽게 요약 할 수 있다.

• Proceedings of the Korea Information Processing Society Conference
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• 2008.05a
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• pp.427-430
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• 2008

본 논문은 비음수 행렬 인수분해(NMF, non-negative matrix factorization)와 NMF 군집방법을 이용하여 다중문서를 요약하는 새로운 방법을 제안하였다. 본 논문에서 NMF에 의해 계산된 의미 특징(semantic feature)은 문서의 고유 구조(inherent structure)를 반영하여 문장을 추출함으로써 요약의 질을 높일 수 있고, 의미 변수(semantic variable)를 이용한 문장의 군집은 문장 간의 유사성과 다양성 고려하여서 쉽게 과잉정보를 제거하여 문장을 요약할 수 있는 장점을 갖는다.

• Journal of the Korea Computer Industry Society
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• v.8 no.4
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• pp.229-236
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• 2007

A factored form is a sum of products of sums of products, ..., of arbitrary depth. Factoring is the process of deriving a parenthesized form with the smallest number of literals from a two-level form of a logic expression. The factored form is not unique and described as either algebraic or Boolean. A Boolean factored form contains fewer number of literals than an algebraic factored form. In this paper, we present a new method for a Boolean factorization. The key idea is to identify two-cube Boolean subexpressions from given two-level logic expression and to extract divisor/quotient pairs. Then, we derive extended divisor/quotient pairs, where their quotients are not cube-free, from the generated divisor/quotients pairs. We generate quotient/quotient pairs from divisor/quotient pairs and extended divisor/quotient pairs. Using the pairs, we make a matrix to generate Boolean factored form based on a technique of rectangle covering.