"Best Approximation in Inner Product Spaces" by Frank Deutsch.
This book is about the following problem,
"Given a point P and a set S in a vector space, find the point in S closest to P."
(The most common example of a vector space is the Cartesian Coordinate Plane which is also called R^2 because every point is of the form (x,y) where x and y are real numbers.)
This book is very simply written. All the details of the proofs are provided. Also, Professor Deutsch covers the history of many of the theorems in the book. Applications to Linear Regression, Interpolation, and Control Systems are given. The main prerequisite for reading the book is a course in mathematical analysis (Rudin or Royden) and a course in matrices or linear algebra. The book is based on the graduate level Approximation Theory course which Dr. Deutsch taught for several years.
This book is about the following problem,
"Given a point P and a set S in a vector space, find the point in S closest to P."
(The most common example of a vector space is the Cartesian Coordinate Plane which is also called R^2 because every point is of the form (x,y) where x and y are real numbers.)
This book is very simply written. All the details of the proofs are provided. Also, Professor Deutsch covers the history of many of the theorems in the book. Applications to Linear Regression, Interpolation, and Control Systems are given. The main prerequisite for reading the book is a course in mathematical analysis (Rudin or Royden) and a course in matrices or linear algebra. The book is based on the graduate level Approximation Theory course which Dr. Deutsch taught for several years.