# Multivariate Polysplines: Applications to Numerical and Wavelet Analysis

## Ognyan Kounchev

0 avg rating
( 0 ratings by Goodreads )

Multivariate polysplines are a new mathematical technique that has arisen from a synthesis of approximation theory and the theory of partial differential equations. It is an invaluable means to interpolate practical data with smooth functions.

Multivariate polysplines have applications in the design of surfaces and "smoothing" that are essential in computer aided geometric design (CAGD and CAD/CAM systems), geophysics, magnetism, geodesy, geography, wavelet analysis and signal and image processing. In many cases involving practical data in these areas, polysplines are proving more effective than well-established methods, such as kKriging, radial basis functions, thin plate splines and minimum curvature.

• Part 1 assumes no special knowledge of partial differential equations and is intended as a graduate level introduction to the topic
• Part 2 develops the theory of cardinal Polysplines, which is a natural generalization of Schoenberg's beautiful one-dimensional theory of cardinal splines
• Part 3 constructs a wavelet analysis using cardinal Polysplines. The results parallel those found by Chui for the one-dimensional case
• Part 4 considers the ultimate generalization of Polysplines - on manifolds, for a wide class of higher-order elliptic operators and satisfying a Holladay variational property

"synopsis" may belong to another edition of this title.

From the Back Cover:

Multivariate Polysplines presents a completely original approach to multivariate spline analysis. Polysplines are piecewise polyharmonic splines and provide a powerful means of interpolating data. Examples in the text indicate that in many practical cases of data smoothing Polysplines are more effective than well-established techniques, such as Kriging, Radial Basis Functions and Minimum Curvature. They also provide new perspectives on wavelet theory with applications to signal and image processing.

Key Features

· Part 1 assumes no special knowledge of partial differential equations and is intended as a graduate level introduction to the topic
· Part 2 develops the theory of cardinal Polysplines, which is a natural generalization of Schoenberg's beautiful one-dimensional theory of cardinal splines.
· Part 3 constructs a wavelet analysis using cardinal Polysplines. The results parallel those found by Chui for the one-dimensional case.
· Part 4 considers the ultimate generalization of Polysplines - on manifolds, for a wide class of higher-order elliptic operators and satisfying a Holladay variational property.

Multivariate Polysplines is aimed principally at specialists in approximation and spline theory, wavelet analysis and signal and image processing. It will also prove a valuable text for people using computer aided geometric design (CAGD and CAD/CAM) systems or smoothing and spline methods in geophysics, geodesy, geology, magnetism etc. as it offers a flexible alternative to traditional tools such as Kriging, Radial Basis Functions and Minimum Curvature.

The book is also suitable as a text for graduate courses on these topics.

Ognyan Kounchev received his M.S. in partial differential equations from Sofia University, Bulgaria and his Ph.D. in optimal control of partial differential equations and numerical methods from the University of Belarus, Minsk. He was awarded a grant from the Volkswagen Foundation (1996-1999) for studying the applications of partial differential equations in approximation and spline theory. Currently, Dr Kounchev is a Fulbright Scholar at the University of Wisconsin-Madison where he works in the Wavelet Ideal Data Representation Center in the Department of Computer Sciences.

Ognyan Kounchev received his M.S. in partial differential equations from Sofia University, Bulgaria and his Ph.D. in optimal control of partial differential equations and numerical methods from the University of Belarus, Minsk. He was awarded a grant from the Volkswagen Foundation (1996-1999) for studying the applications of partial differential equations in approximation and spline theory. Currently, Dr Kounchev is a Fulbright Scholar at the University of Wisconsin-Madison where he works in the Wavelet Ideal Data Representation Center in the Department of Computer Sciences.

£ 72.45

Shipping: FREE
From United Kingdom to U.S.A.

Destination, Rates & Speeds

## 1.Multivariate Polysplines: Applications to Numerical and Wavelet Analysis (Hardback)

ISBN 10: 0124224903 ISBN 13: 9780124224902
New Hardcover Quantity Available: 1
Seller:
The Book Depository
(London, United Kingdom)
Rating

Book Description Elsevier Science Publishing Co Inc, United States, 2001. Hardback. Book Condition: New. Language: English . Brand New Book. Multivariate polysplines are a new mathematical technique that has arisen from a synthesis of approximation theory and the theory of partial differential equations. It is an invaluable means to interpolate practical data with smooth functions. Multivariate polysplines have applications in the design of surfaces and smoothing that are essential in computer aided geometric design (CAGD and CAD/CAM systems), geophysics, magnetism, geodesy, geography, wavelet analysis and signal and image processing. In many cases involving practical data in these areas, polysplines are proving more effective than well-established methods, such as kKriging, radial basis functions, thin plate splines and minimum curvature. Bookseller Inventory # AA59780124224902

£ 72.45
Convert Currency
Shipping: FREE
From United Kingdom to U.S.A.
Destination, Rates & Speeds

## 2.Multivariate Polysplines: Applications to Numerical and Wavelet Analysis (Hardback)

ISBN 10: 0124224903 ISBN 13: 9780124224902
New Hardcover Quantity Available: 1
Seller:
The Book Depository US
(London, United Kingdom)
Rating

Book Description Elsevier Science Publishing Co Inc, United States, 2001. Hardback. Book Condition: New. Language: English . Brand New Book. Multivariate polysplines are a new mathematical technique that has arisen from a synthesis of approximation theory and the theory of partial differential equations. It is an invaluable means to interpolate practical data with smooth functions. Multivariate polysplines have applications in the design of surfaces and smoothing that are essential in computer aided geometric design (CAGD and CAD/CAM systems), geophysics, magnetism, geodesy, geography, wavelet analysis and signal and image processing. In many cases involving practical data in these areas, polysplines are proving more effective than well-established methods, such as kKriging, radial basis functions, thin plate splines and minimum curvature. Bookseller Inventory # AA59780124224902

£ 76.43
Convert Currency
Shipping: FREE
From United Kingdom to U.S.A.
Destination, Rates & Speeds

## 3.Multivariate Polysplines: Applications to Numerical and Wavelet Analysis

ISBN 10: 0124224903 ISBN 13: 9780124224902
New Hardcover Quantity Available: 1
Seller:
Ergodebooks
(RICHMOND, TX, U.S.A.)
Rating

Book Description Academic Press, 2001. Hardcover. Book Condition: New. 1. Bookseller Inventory # DADAX0124224903

£ 76.11
Convert Currency
Shipping: £ 3.03
Within U.S.A.
Destination, Rates & Speeds

## 4.MULTIVARIATE POLYSPLINES

ISBN 10: 0124224903 ISBN 13: 9780124224902
New Paperback Quantity Available: 1
Print on Demand
Seller:
Ria Christie Collections
(Uxbridge, United Kingdom)
Rating

Book Description Elsevier, 2016. Paperback. Book Condition: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Bookseller Inventory # ria9780124224902_lsuk

£ 98.58
Convert Currency
Shipping: £ 3.87
From United Kingdom to U.S.A.
Destination, Rates & Speeds

## 5.Multivariate Polysplines: Applications to Numerical and Wavelet Analysis

ISBN 10: 0124224903 ISBN 13: 9780124224902
New Hardcover Quantity Available: 1
Seller:
Revaluation Books
(Exeter, United Kingdom)
Rating

Book Description Academic Pr, 2001. Hardcover. Book Condition: Brand New. 1st edition. 498 pages. 10.00x7.00x1.00 inches. In Stock. Bookseller Inventory # __0124224903

£ 98.32
Convert Currency
Shipping: £ 6
From United Kingdom to U.S.A.
Destination, Rates & Speeds

## 6.Multivariate Polysplines

ISBN 10: 0124224903 ISBN 13: 9780124224902
New Quantity Available: 4
Print on Demand
Seller:
Majestic Books
(London, ,, United Kingdom)
Rating

Book Description Elsevier. Book Condition: New. pp. 498 This item is printed on Demand. Bookseller Inventory # 8340831

£ 101.43
Convert Currency
Shipping: £ 5.50
From United Kingdom to U.S.A.
Destination, Rates & Speeds

## 7.Multivariate Polysplines

ISBN 10: 0124224903 ISBN 13: 9780124224902
New Hardcover Quantity Available: 1
Seller:
Herb Tandree Philosophy Books
(Stroud, GLOS, United Kingdom)
Rating

Book Description Academic Press, 2001. Hardback. Book Condition: NEW. 9780124224902 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Bookseller Inventory # HTANDREE01198665

£ 100
Convert Currency
Shipping: £ 8
From United Kingdom to U.S.A.
Destination, Rates & Speeds

## 8.Multivariate Polysplines

ISBN 10: 0124224903 ISBN 13: 9780124224902
New Hardcover Quantity Available: 1
Seller:
Herb Tandree Philosophy Books
(Stroud, GLOS, United Kingdom)
Rating

Book Description Academic Press, 2001. Hardback. Book Condition: NEW. 9780124224902 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Bookseller Inventory # HTANDREE0894721

£ 100
Convert Currency
Shipping: £ 8
From United Kingdom to U.S.A.
Destination, Rates & Speeds

## 9.Multivariate Polysplines: Applications to Numerical and Wavelet Analysis

ISBN 10: 0124224903 ISBN 13: 9780124224902
New Hardcover First Edition Quantity Available: 1
Seller:
Irish Booksellers
(Rumford, ME, U.S.A.)
Rating

Book Description Academic Press, 2001. Hardcover. Book Condition: New. book. Bookseller Inventory # M0124224903

£ 111.68
Convert Currency
Shipping: FREE
Within U.S.A.
Destination, Rates & Speeds

## 10.Multivariate Polysplines: Applications to Numerical and Wavelet Analysis

ISBN 10: 0124224903 ISBN 13: 9780124224902
New Hardcover Quantity Available: 5
Seller:
Ergodebooks
(RICHMOND, TX, U.S.A.)
Rating

Book Description Academic Press, 2001. Hardcover. Book Condition: New. Bookseller Inventory # INGM9780124224902