Matrix Theory and Algorithms

Handbook of Mathematical Functions

Convex Optimization

Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.

Handbook of Mathematical Functions

Handbook of Mathematical Functions

The Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables was the culmination of a quarter century of National Bureau of Standards (NBS) work on core mathematical tools. Evaluating commonly occurring mathematical functions has been a fundamental need as long as mathematics has been applied to the solution of practical problems. In 1938, NBS initiated its Mathematical Tables Project to satisfy the increasing demand for extensive and accurate tables of functions. The Handbook project occurred during the period when general-purpose electronic computing machinery was first coming into use in government research laboratories. A number of difficult mathematical problems that emerged in the course of developing the Handbook engaged researchers in the NBS Applied Mathematics Division for a number of years after its publication. Two of these are especially noteworthy, the first having to do with stability of computations and the second with precision.

Handbook of Mathematical Functions.

Green's Function Theory for the Anderson Model

Journal of the Physical Society of Japan 69 (2000) pp. 1449-1456 Kondo Resonance in a Quantum Dot: Finite-U Anderson Model out of Equilibrium Daichi Matsumoto Progress of Theoretical Physics Vol. 43 No. 6 (1970) pp. 1458-1479 Self-Consistent Treatment of Anderson Model and Magnetic Susceptibility Hiroshi Mamada and Fumihiko Takano Progress of Theoretical Physics Vol. 44 No. 1 (1970) pp. 59-76 Self-Consistent Treatment of the Wolff-Moriya Model Fumiaki Shibata and Hiroshi Mamada Progress of Theoretical Physics Vol. 45 No. 4 (1971) pp. 1028-1049 On the Singularity in Anderson Model. I Hiroshi Mamada and Fumiaki Shibata

The Scattering Matrix Method in the Linear Chain

Progress of Theoretical Physics Vol. 55 No. 1 (1976) pp. 10–20 Localized Spin Wave State in a One-Dimensional Heisenberg Ferromagnet with a Boundary and Impurity Spins Yoshihiro Tsuchida