Computational Complexity Of Solving Equation Systems
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Computational Complexity of Solving Equation Systems
This volume considers the computational complexity of determining whether a system of equations over a fixed algebra A has a solution. It examines in detail the two problems this leads to: SysTermSat(A) and SysPolSat(A), in which equations are built out of terms or polynomials, respectively. The book characterizes those algebras for which SysPolSat can be solved in a polynomial time. So far, studies and their outcomes have not covered algebras that generate a variety admitting type 1 in the sense of Tame Congruence Theory. Since unary algebras admit only type 1, this book focuses on these algebras to tackle the main problem. It discusses several aspects of unary algebras and proves that the Constraint Satisfaction Problem for relational structures is polynomially equivalent to SysTermSat over unary algebras. The book’s final chapters discuss partial characterizations, present conclusions, and describe the problems that are still open.
Numerical Methods in Finance
Author: Paolo Brandimarte
language: en
Publisher: John Wiley & Sons
Release Date: 2003-09-29
Balanced coverage of the methodology and theory of numerical methods in finance Numerical Methods in Finance bridges the gap between financial theory and computational practice while helping students and practitioners exploit MATLAB for financial applications. Paolo Brandimarte covers the basics of finance and numerical analysis and provides background material that suits the needs of students from both financial engineering and economics perspectives. Classical numerical analysis methods; optimization, including less familiar topics such as stochastic and integer programming; simulation, including low discrepancy sequences; and partial differential equations are covered in detail. Extensive illustrative examples of the application of all of these methodologies are also provided. The text is primarily focused on MATLAB-based application, but also includes descriptions of other readily available toolboxes that are relevant to finance. Helpful appendices on the basics of MATLAB and probability theory round out this balanced coverage. Accessible for students-yet still a useful reference for practitioners-Numerical Methods in Finance offers an expert introduction to powerful tools in finance.
Intelligent Systems Modeling and Simulation II
Author: Samsul Ariffin Abdul Karim
language: en
Publisher: Springer Nature
Release Date: 2022-10-12
This book develops a new system of modeling and simulations based on intelligence system. As we are directly moving from Third Industrial Revolution (IR3.0) to Fourth Industrial Revolution (IR4.0), there are many emergence techniques and algorithm that appear in many sciences and engineering branches. Nowadays, most industries are using IR4.0 in their product development as well as to refine their products. These include simulation on oil rig drilling, big data analytics on consumer analytics, fastest algorithm for large-scale numerical simulations and many more. These will save millions of dollar in the operating costs. Without any doubt, mathematics, statistics and computing are well blended to form an intelligent system for simulation and modeling. Motivated by this rapid development, in this book, a total of 41 chapters are contributed by the respective experts. The main scope of the book is to develop a new system of modeling and simulations based on machine learning, neural networks, efficient numerical algorithm and statistical methods. This book is highly suitable for postgraduate students, researchers as well as scientists that have interest in intelligent numerical modeling and simulations.