A new class of methods, termed "group explicit methods," is introduced in this text. Their applications to solve parabolic, hyperbolic and elliptic equations are outlined, and the advantages for their implementation on parallel computers clearly portrayed. Also included are the introductory and fundamental concepts from which the new methods are derived, and on which they are dependent. With the increasing advent of parallel computing into all aspects of computational mathematics, there is no doubt that the new methods will be widely used.

Central to the future direction of mankind on planet Earth is the belief that the origination and design of the Universe and the plan by which it operates are the work of one almighty creator. If one follows the view that a motor car comes into existence by way of the design and manufacture process or that a building is the end result of the design and construct process, then it is a simple progression to believe that the Universe and its modus operandi were designed and brought into existence by one superior being. Peter Vanser, an avid star gazer and amateur astronomer, has for several months been watching rapidly moving lights over the Pacific Ocean off the Gold Coast in Australia. The Commanding Officer of a mission from the Planet Gronorg, in the Orion Constellation, has been attempting to communicate with Earthian leaders via coded transmissions, all to no avail.The mission commander, Mar Zedok, wants to land on Earth to convey important information on an impending attack by an aggressive alien civilization. Vanser is approached personally by a Gronorgan operative and is invited to visit Gronorg to experience their social fabric and intelligence.

Central to the future direction of mankind on planet Earth is the belief that the origination and design of the Universe and the plan by which it operates are the work of one almighty creator. If one follows the view that a motor car comes into existence by way of the design and manufacture process or that a building is the end result of the design and construct process, then it is a simple progression to believe that the Universe and its modus operandi were designed and brought into existence by one superior being. Peter Vanser, an avid star gazer and amateur astronomer, has for several months been watching rapidly moving lights over the Pacific Ocean off the Gold Coast in Australia. The Commanding Officer of a mission from the Planet Gronorg, in the Orion Constellation, has been attempting to communicate with Earthian leaders via coded transmissions, all to no avail.The mission commander, Mar Zedok, wants to land on Earth to convey important information on an impending attack by an aggressive alien civilization. Vanser is approached personally by a Gronorgan operative and is invited to visit Gronorg to experience their social fabric and intelligence.

Presenting the main recent advances made in parallel processing, this volume focuses on the design and implementation of systolic algorithms as efficient computational structures that encompass both multiprocessing and pipelining concepts.;While the architecture of present-day parallel supercomputers is largely based on the concept of a shared memory, with its attendant limitations of common access, advances in semiconductor technology have led to the development of highly parallel computer architectures with decentralized storage and limited connections in which each processor possesses high bandwidth local memory connected to a small number of neighbours. Systolic arrays are a typical and highly efficient example of such architectures, enabling cost effective, high-speed parallel processing for large volumes of data, with ultra-high throughput rates. Algorithms suitable for implementation on systolic arrays find applications in areas such as signal and image processing, pattern matching, linear algebra, recurrence algorithms and graph problems.