Fractional Calculus (Mathematics in Science and Engineering, Vol. 111)

by Keith B. Oldham, Jerome Spanier

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.

- Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering

Genres: Mathematics, Reference

322 pages, Hardcover

First published June 1, 1974

Reviews

[Jafet]

Es un libro que se me complico bastante ya que está construido con el enfoque de usar series hipergeométricas, pero tiene temas interesantes debido a que la mitad del libro son ejemplos de aplicación de la teoría fraccionaria a química y física. En particular me gusto como a partir de la integral de Cauchy define la integral fraccionaria sin recurrir al clásico método de integración repetida ni depender del teorema de Fubini de intercambio del orden de integrales

[Michael · Rating 4 out of 5]

Lots of neat formulas about hypergeometric functions, but it felt disjointed - like it was a series of papers stapled together.

If you read it, I recommend reading the chapters in the order: 1, 2, 3, 5, 9, 4, 6, 7, 10, 8, 11.