More importantly, a variant of it is seen to work desirably in certain singular situations where the celebrated inequality appears to. The wellknown cauchyschwarz inequality is cs atabtb atb2 8a. Zentralblatt fur mathematik the classic work in this field is hardy, littlewood. Check out for course materials, and information regarding updates on each of the courses. Later the integral inequality was rediscovered by hermann amandus schwarz 1888. Closedform cauchyschwarz pdf divergence for mixture of. Void probabilities and cauchyschwarz divergence for. Verify the cauchyschwarz inequality and the triangle inequality for the given vectors and inner product. The inequality for sums was published by augustinlouis cauchy 1821, while the corresponding inequality for integrals was first proved by viktor bunyakovsky 1859. Using the cauchyschwarz inequality as a guide, steele presents a fascinating collection of problems related to inequalities and coaches readers through solutions, in a style reminiscent of george polya, by teaching basic concepts and sharpening problem solving skills at the same.
Cauchy schwarz inequality as the initial guide, the reader is led through a sequence of fascinating problems whose solutions are presented as they might have been discovered either by one of historys famous mathe. The cauchy schwarz divergence is based on the cauchy schwarz inequality for inner products, and is defined for two random vectors with probability densities f and g by 23 d cs f, g. Aditional problems on cauchy schwarz inequality youtube. Problem solving strategies by arthur engel contains significant material on inequalities. Nowinski, 9781468439281, available at book depository with free delivery worldwide. Also, as cauchy sequences are bounded its not possible for the 2 condition to hold. One obtains the cauchy schwarz inequality as a special case. Some problems on cauchy schwarz inequality best books on mathematical inequalities inequalities a mathematical olympiad approach metho.
The comparative simulation results and conclusions are given in section iv and section v, respectively. Numerous variants and generalizations of this inequality are known. An introduction to the art of mathematical inequalities maa problem books at. The cauchyschwarz divergence for poisson point processes. Applications of functional analysis in engineering. An introduction to the art of mathematical inequalities by j. For example, the following inequalities are straightforward. Applications of functional analysis in engineering by j.
Can the cauchy product of divergent series with itself be convergent. In this note we consider generalizations to four vectors. The cauchy schwarz master class this lively, problemoriented text is designed to coach readers toward mastery of the most fundamental mathematical inequalities. Michael steele, 9780521546775, available at book depository with free delivery worldwide. A convex cauchyschwarz divergence measure for blind. In this paper, we extend the notion of cauchyschwarz divergence to point processes and establish that the cauchyschwarz divergence. This paper contributes a tutorial level discussion of some interesting properties of the recent cauchyschwarz cs divergence measure.
An introduction to the art of mathematical inequalities maa problem books series. Cy420steelefm cy420steele 0 0521837758 january 16, 2004. This paper contributes a tutorial level discussion of some interesting properties of the recent cauchyschwarz cs divergence measure between probability. Glmb, while the proposed analytic cauchyschwarz divergence. Index proof of, 394 ceiling function, 529539 cellular automaton, xvii center of a circle, 126 of a hyperbola, 142 of an ellipse, 129 chebyshevs inequality, 412. A sequence zn converges if and only if it is a cauchy sequence. A brief description of previous divergence measures divergence, or the related dissimilarity, measures play an. Complex sequences and series let c denote the set x,y.