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Generalized Inverses
1. The Inverse of a Nonsingular Matrix It is well known that every nonsingular matrix A has a unique inverse, ?1 denoted by A , such that ?1 ?1 AA = A A =I, (1) where I is the …
Orthogonal Polynomials for Exponential Weights
The analysis of orthogonal polynomials associated with general weights was a major theme in classical analysis in the twentieth century, and undoubtedly will continue to grow in …
Solving the Pell Equation
Pell’s Equation is a very simple Diophantine equation that has been known to mathematicians for over 2000 years. Even today research involving this equation continues to be very …
Biorthogonal Systems in Banach Spaces
One of the fundamental questions of Banach space theory is whether every Banach space has a basis. A space with a basis gives us a sense of familiarity and concreteness, and …
Differentiable Optimization and Equation Solving
In 1984, N. Karmarkar published a seminal paper on algorithmic linear programming. During the subsequent decade, it stimulated a huge outpouring of new algorithmic results by …
Interpolation and Sidon Sets for Compact Groups
Understanding special sets of integers was classically of interest to Hadamard, Zygmund and others, and continues to be of interest today. This book is a modern treatment of the …
Convex Analysis and Nonlinear Optimization
Optimization is a rich and thriving mathematical discipline. The theory underlying current computational optimization techniques grows ever more sophisticated. The powerful and …
Interpolation and Approximation by Polynomials
This book is intended as a course in numerical analysis and approximation theory for advanced undergraduate students or graduate students, and as a reference work for those who …
Mathematics and the Aesthetic
A majority of the chapters in this book first saw the light of day as talks at a conference organised and held at Queen’s University in Kingston, Ontario, Canada in April 2001. …
Combinatorial Methods
This book is about three seemingly independent areas of mathematics: combinatorial group theory, the theory of Lie algebras and affine algebraic geometry. Indeed, for many years …
Reflection Groups and Invariant Theory
Reflection Groups and their invariant theory provide the main themes of this book and the first two parts focus on these topics. The first 13 chapters deal with reflection groups …
Best Approximation in Inner Product Spaces
This book evolved from notes originally developed for a graduate course, "Best Approximation in Normed Linear Spaces," that I began giving at Penn State Uni versity more than 25 …