ABSTRACT
This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book focuses on spectral analysis with the main goal of attempting to convey to the reader some of the common aspects, strategies and mathematical methods in seemingly disjoint research fields. It explores a reliable procedure is designed to ensure stability of the Pade approximant by having to deal only with stable or Schur polynomials in the Pade numerator and denominator. The book elaborates the Pade–Schur approximant, with a rational polynomial ansatz which can be generated in any of the selected procedures including the Lanczos algorithm. It illuminates the quantum-mechanical tight binding model or, equivalently the nearest neighbour approximation, using spectral analysis based upon the Lanczos recursive algorithm. The book carries out spectral analysis from the viewpoint of the power, modified and mixed moment problems.
