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On Optimal Short Recurrences for Generating Orthogonal Krylov Subspace Bases
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| Pengarang | : | L. Suwanto |
| Nama Majalah/Jurnal | : | Siam Review |
| Volume / Edisi | : | 50-3, SEPTEMBER (No. 3) |
| Halaman | : | 485-503 |
| Abstrak | : | We analyze necessary and sufficient conditions on a nonsingular matrix A such that, for any initial vector , an orthogonal basis of the Krylov subspaces is generated by a short recurrence. Orthogonality here is meant with respect to some unspecified positive definite inner product. This question is closely related to the question of existence of optimal Krylov subspace solvers for linear algebraic systems, where optimal means the smallest possible error in the norm induced by the given inner product. The conditions on A we deal with were first derived and characterized more than 20 years ago by Faber and Manteuffel (SIAM J. Numer. Anal., 21 (1984), pp. 352–362). Their main theorem is often quoted and appears to be widely known. Its details and underlying concepts, however, are quite intricate, with some subtleties not covered in the literature we are aware of. Our paper aims to present and clarify the existing important results in the context of the Faber–Manteuffel theorem. Furthermore, we review attempts to find an easier proof of the theorem and explain what remains to be done in order to complete that task. |
Singularly Perturbed Linear Two-Point Boundary Value Problems
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Review |
| Volume / Edisi | : | 50-3, SEPTEMBER (No. 3) |
| Halaman | : | 459-482 |
| Abstrak | : | Finding asymptotic solutions to two-point boundary value problems for linear singularly perturbed second-order ordinary differential equations is now quite well understood. Troublesome exceptions involving turning points, known as problems of boundary layer resonance, have been studied by many experts since the initial work of Ackerberg and O'Malley [Stud. Appl. Math., 49 (1970), pp. 277–295]; this significant work is surveyed here. Closely related literature involves the canard phenomena. New, generally more geometric, approaches, including Gevrey asymptotics and “blowup," promise improved understanding of such sensitive asymptotics and their generalizations. |
Estimation of Subspace Arrangements with Applications in Modeling and Segmenting Mixed Data
| Pengarang | : | Yi Ma,W. Dean Pesnell |
| Nama Majalah/Jurnal | : | Siam Review |
| Volume / Edisi | : | 50-3, SEPTEMBER (No. 3) |
| Halaman | : | 413-458 |
| Abstrak | : | Recently many scientific and engineering applications have involved the challenging task of analyzing large amounts of unsorted high-dimensional data that have very complicated structures. From both geometric and statistical points of view, such unsorted data are considered mixed as different parts of the data have significantly different structures which cannot be described by a single model. In this paper we propose to use subspace arrangements—a union of multiple subspaces—for modeling mixed data: each subspace in the arrangement is used to model just a homogeneous subset of the data. Thus, multiple subspaces together can capture the heterogeneous structures within the data set. In this paper, we give a comprehensive introduction to a new approach for the estimation of subspace arrangements. This is known as generalized principal component analysis (GPCA). In particular, we provide a comprehensive summary of important algebraic properties and statistical facts that are crucial for making the inference of subspace arrangements both efficient and robust, even when the given data are corrupted by noise or contaminated with outliers. This new method in many ways improves and generalizes extant methods for modeling or clustering mixed data. There have been successful applications of this new method to many real-world problems in computer vision, image processing, and system identification. In this paper, we will examine several of those representative applications. This paper is intended to be expository in nature. However, in order that this may serve as a more complete reference for both theoreticians and practitioners, we take the liberty of filling in several gaps between the theory and the practice in the existing literature. |
The HDTV Grand Alliance system
| Pengarang | : | E. Petajan |
| Nama Majalah/Jurnal | : | Proceedings of the IEEE |
| Volume / Edisi | : | 83-7, JULY (No. 7) |
| Halaman | : | 1094-1105 |
| Abstrak | : | The Grand Alliance (GA) was formed to define and construct a system for the delivery of HDTV using terrestrial broadcast channels. This system is composed of the best components from previously competing systems considered by the FCC. MPEG-2 syntax is used with novel encoding techniques to deliver a set of video scanning formats for a variety of applications. The paper focuses on video compression technology and also describes the important features and concepts embodied in the GA system as compared to the previous digital HDTV systems. |
High definition television systems
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Proceedings of the IEEE |
| Volume / Edisi | : | 83-7, JULY (No. 7) |
| Halaman | : | 1086-1093 |
| Abstrak | : | High definition television (HDTV) services will play the most important role in the digital television systems for the future. HDTV is already broadcast daily in Japan and advanced television (ATV) standards will soon be established in the US. The hardware systems for two HDTV systems, the 1125/60 and 1250/50 systems, have already been developed. Their outlines are described in the paper. Signal processing of HDTV is mainly carried out by digital methods on both the studio and receiver sides. The principles of processing are the same as for conventional television but the higher clock frequency and larger quantity of information require more sophisticated hardware. Digital signal processing methods are the key technology in HDTV broadcasting systems regardless of whether modulation is analog or digital. Some broadcasting systems are already practical use while others, are experimental. The author discusses these systems. The aim of the article is to present a global scope of the HDTV technology. |
Interactive television
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Proceedings of the IEEE |
| Volume / Edisi | : | 83-7, JULY (No. 7) |
| Halaman | : | 1071-1085 |
| Abstrak | : | Interactive television (ITV) is a new form of residential consumer video service that gives viewers far greater control over the contents of programs than is possible with conventional television. There are substantial technical challenges to offering a ITV service on a large scale, both in content creation and delivery. The paper discusses those challenges and presents a new system architecture for offering ITV, along with a broad range of other interactive video services, to consumers in their homes. A new suite of tools to simplify the creation of compelling interactive programming is also described. |
VLSI for digital television
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Proceedings of the IEEE |
| Volume / Edisi | : | 83-7, JULY (No. 7) |
| Halaman | : | 1055-1070 |
| Abstrak | : | The paper provides an overview of the current status in the industry of digitized television including techniques used and their limitations, technological concerns and design methodologies needed to achieve the goals for highly integrated systems. A multiresolution scalable generic HDTV codec based on subband coding is presented, proving the feasibility of VLSI for true HDTV frequency. In addition, a VLSI design methodology is proposed based on programmable processor macrofunctions optimized for the huge amount of data to be processed. The goal was to integrate general VLSI implementation aspects in a specific digital codec system to validate the design methodology for high speed multimedia applications. Digital TV functions can be optimized for encoding and decoding in the same conceptual process and be implemented in silicon in a mole dedicated way using a kind of automated custom design approach allowing enough flexibility. |
Digital video recording
| Pengarang | : | M. Umemoto |
| Nama Majalah/Jurnal | : | Proceedings of the IEEE |
| Volume / Edisi | : | 83-7, JULY (No. 7) |
| Halaman | : | 1044-1054 |
| Abstrak | : | Through mutual technology transfer between consumer and professional video recorders, the last 20 years has witnessed a rapid evolution from analog to digital recording. Each new digital videotape recorder (VTR) uses different channel coding. This implies that improving the recording density involves the development of new channel-coding schemes together with evolutionary magnetic tapes and heads. As a result, professional digital VTR's offer the best features for video recording. This paper reviews state-of-the-art magnetic recording devices, signal processing techniques for digital recording. It also describes the specifications for home-use digital recorders for current television systems, and discusses disk recording technology in the future. |
Cameras and display systems
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Proceedings of the IEEE |
| Volume / Edisi | : | 83-7, JULY (No. 7) |
| Halaman | : | 1032-1043 |
| Abstrak | : | We first discuss the position of cameras and displays in digital television systems. It is difficult to realize these devices in digital form so cameras and displays will remain analog for some time, even after television signal processing is implemented digitally. Nevertheless, the importance of camera and display in television systems will not diminish. These devices will always be key elements in the human interface. Second, we describe the current state of the art and future trends in camera and display technology. In addition to providing an overview of the charge coupled device (CCD), we discuss the digital technologies used in a CCD camera. We also provide an overview of currently available displays-CRT's, flat panel displays, projection displays, and head-mounted displays (HMD's)-and discuss future possible lines of research. Finally, we discuss camera and display technology as applied to digital television systems, including the use of these devices in a multimedia environment. |
Digital actors for interactive television
| Pengarang | : | N. Magnenat Thalmann |
| Nama Majalah/Jurnal | : | Proceedings of the IEEE |
| Volume / Edisi | : | 83-7, JULY (No. 7) |
| Halaman | : | 1022-1031 |
| Abstrak | : | In this paper, we define the concept of digital actors and show their importance in the future interactive digital television and multimedia. We discuss the applications of these digital actors in the new multimedia services especially for training and education. We summarize the main techniques to create and control these digital actors and emphasize the importance to develop new tools for the control and the autonomy of these actors. An integrated and functional system for the animation of digital actors is presented. In particular, we describe the integration of motion control techniques, autonomy based on synthetic sensors and facial communication. |