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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."

"ABSTRAK"Sifat-sifat spektral dari matrik nonnegatif dan matrikirreducible seperti radius spektral eigenvalue dan eigenvektorsangat penting dan bermanfaat dalam berbagai disiplinilmu."Salah satu penggunaan sifat spektral dari matrik nonnegatifadalah dalam peibahasan suatu bentuk matrik khusus yang disebutMatrik H.Model input-output dalam perekonoiiian suatu jiasyarakatdinyatakansecara mateaatis dan dalam model matematis tersebutterbentuk matrik HHelalul sifat matrik H mudah dianalisis apakah model perekonoEiantersebut feasible dan profitable.

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"ABSTRAKBerkembangnya portal berita online di Indonesia sangat pesat sehingga menyebabkan meningkatnya arus informasi. Banyaknya informasi yang ada pada portal berita online menimbulkan kesulitan untuk mengetahui topik berita secara garis besar. Untuk itu diperlukan ekstraksi topik berita online yang dapat dilakukan secara otomatis dengan bantuan mesin. Salah satu metode yang dapat digunakan untuk mengekstraksi topik berita online secara otomatis adalah Non-Negative Matrix Factorization (NMF). Pada umumnya algoritma NMF menggunakan inisialisasi random untuk mendekomposisi matriks. Inisialisasi random pada algoritma NMF menghasilkan topik berita yang berbeda setiap kali eksekusi. Pada penelitian ini akan diimplentasikan salah satu metode inisialisasi NMF yaitu Non-Negative Double Singular Value Decomposition (NNDSVD). Metode ini berdasarkan dua proses dari Singular Value Decomposition (SVD). Proses SVD yang pertama untuk pendekatan matriks data dan yang kedua untuk pendekatan bagian positif. NNDSVD tidak mengandung unsur random, sehingga menghasilkan topik berita yang sama setiap kali eksekusi.

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ABSTRACTThe rapid development of portal online news in Indonesia causes the increment of information flow. The amount of information contained in these portals makes it difficult to know the outline of news topic. So, it is necessary to extract the topic automatically by using machine. Non-Negative Matrix Factorization (NMF) is a method used to extract news topic automatically. Generally, NMF algorithm uses random initialization to decompose matrix to get different news topic in every execution. In this research, one of NMF initialization, Non-negative Double Singular Value Decomposition (NNDSVD), will be implemented. This method uses two processes from Singular Value Decomposition (SVD), one approximating the data matrix, the other approximating positive section. NNDSVD contains no randomization, so that produce same news topic in every execution."

"This book is the first to pay special attention to the combined issues of speed and numerical reliability in algorithm development. These two requirements have often been regarded as competitive, so much so that the design of fast and numerically reliable algorithms for large-scale structured systems of linear equations, in many cases, remains a significant open issue. Fast Reliable Algorithms for Matrices with Structure helps bridge this gap by providing the reader with recent contributions written by leading experts in the field.The authors deal with both the theory and the practice of fast numerical algorithms for large-scale structured linear systems. Each chapter covers in detail different aspects of the most recent trends in the theory of fast algorithms, with emphasis on implementation and application issues. Both direct and iterative methods are covered.This book is not merely a collection of articles. The editors have gone to considerable lengths to blend the individual papers into a consistent presentation. Each chapter exposes the reader to some of the most recent research while providing enough background material to put the work into proper context."

"This self-contained introduction to the behavior of several spectral characteristics of large Toeplitz band matrices is the first systematic presentation of a relatively large body of knowledge. Covering everything from classic results to the most recent developments, Spectral Properties of Banded Toeplitz Matrices is an important resource. The spectral characteristics include determinants, eigenvalues and eigenvectors, pseudospectra and pseudomodes, singular values, norms, and condition numbers. Toeplitz matrices emerge in many applications and the literature on them is immense. They remain an active field of research with many facets, and the material on banded ones until now has primarily been found in research papers."