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"Here is a valuable text and research tool for scientists and engineers who use or work with theory and computation associated with practical problems relating to Markov chains and queuing networks, economic analysis, or mathematical programming. Originally published in 1979, this new edition adds material that updates the subject relative to developments from 1979 to 1993.Theory and applications of nonnegative matrices are blended here, and extensive references are included in each area. You will be led from the theory of positive operators via the Perron-Frobenius theory of nonnegative matrices and the theory of inverse positivity, to the widely used topic of M-matrices. On the way, semigroups of nonnegative matrices and symmetric nonnegative matrices are discussed. Later, applications of nonnegativity and M-matrices are given; for numerical analysis the example is convergence theory of iterative methods, for probability and statistics the examples are finite Markov chains and queuing network models, for mathematical economics the example is input-output models, and for mathematical programming the example is the linear complementarity problem.Nonnegativity constraints arise very naturally throughout the physical world. Engineers, applied mathematicians, and scientists who encounter nonnegativity or generalizations of nonegativity in their work will benefit from topics covered here, connecting them to relevant theory. Researchers in one area, such as queuing theory, may find useful the techniques involving nonnegative matrices used by researchers in another area, say, mathematical programming."

"ABSTRAKPerkembangan teknologi khususnya internet berkembang begitu pesat dewasa ini. Oleh karena itu, arus informasi meningkat begitu cepat yang menyebabkan informasi diperoleh sangat banyak. Media sosial pun menjadi salah satu sarana penyedia informasi, salah satunya adalah Twitter. Pendeteksian topik menjadi suatu kebutuhan bagi masyarakat untuk mengetahui hal-hal yang bicarakan pada waktu tertentu. Maka, dibutuhkan suatu cara yang cepat dan tepat untuk mendapatkan topik dari tweet yang terkirim pada Twitter. Dengan jumlah dokumen yang sangat besar, diperlukan suatu metode otomatis. Salah satu metode otomatis untuk pendeteksian topik adalah model yang berbasis faktorisasi matriks yaitu Non-negative Matrix Factorization (NMF). Metode NMF yang digunakan pada penelitian ini difokuskan pada wilayah Jakarta dan sekitarnya guna melihat topik yang dibahas masyarakat Jakarta dan sekitarnya pada kurun waktu tertentu. Hasil yang didapatkan lewat metode NMF ini selanjutnya akan dievaluasi dengan cara melihat tingkat akurasi yang dihasilkan lalu disimulasikan dalam bentuk tren berdasarkan frekuensi masing-masing topik.

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ABSTRACTDevelopment of technology spesifically in internet grows so fast nowadays. Therefore, flow of information increase rapidly that leads information to be obtained so much. Social media become the one information provider, such as Twitter. Topic detection become a public society to know the things that being discussed at a certain time. Hence, needed a quick and precise method to obatain topic from tweet posted from twitter. With large amount of document, needed an automaticly method. One of automaticly method that based on matrix factorization is Non-negative Matrix Factorization as usually being called as NMF. Non-negative matrix factorization method on this research focused on region of Jakarta in order to know what are being discussed by society there in a period of time. The result have been obtain with NMF method will be evaluated by calculating the accuracy and finally will be simulated in the form of trend plot based on the frequency of the topic."