Yuesheng Xu's Books

Multiscale Methods for Fredholm Integral Equations

By: Zhongying Chen,Charles A. Micchelli,Yuesheng Xu

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Multiscale Methods for Fredholm Integral Equations

By: Zhongying Chen,Charles A. Micchelli,Yuesheng Xu

The recent appearance of wavelets as a new computational tool in applied mathematics has given a new impetus to the field of numerical analysis of Fredholm integral equations. This book gives an account of the state of the art in the study of fast multiscale methods for solving these equations based on wavelets. The authors begin by introducing essential concepts and describing conventional numerical methods. They then develop fast algorithms and apply these to solving linear, nonlinear Fredholm integral equations of the second kind, ill-posed integral equations of the first kind and eigen-problems of compact integral operators. Theorems of functional analysis used throughout the book are summarised in the appendix. The book is an essential reference for practitioners wishing to use the new techniques. It may also be used as a text, with the first five chapters forming the basis of a one-semester course for advanced undergraduates or beginning graduates.

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Page Count

551

Publisher

Cambridge University Press

Published Date

ISBN 10

1316381307

ISBN 13

9781316381304

Generalized Mercer Kernels and Reproducing Kernel Banach Spaces

By: Yuesheng Xu,Qi Ye

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Generalized Mercer Kernels and Reproducing Kernel Banach Spaces

By: Yuesheng Xu,Qi Ye

This article studies constructions of reproducing kernel Banach spaces (RKBSs) which may be viewed as a generalization of reproducing kernel Hilbert spaces (RKHSs). A key point is to endow Banach spaces with reproducing kernels such that machine learning in RKBSs can be well-posed and of easy implementation. First the authors verify many advanced properties of the general RKBSs such as density, continuity, separability, implicit representation, imbedding, compactness, representer theorem for learning methods, oracle inequality, and universal approximation. Then, they develop a new concept of generalized Mercer kernels to construct p-norm RKBSs for 1≤p≤∞ .

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Page Count

134

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470435500

ISBN 13

9781470435509

Rainbow

By: Bai Yuesheng

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Rainbow

By: Bai Yuesheng

Rainbow is presented in the form of novel to show the social reality, national changes, and political situations in China over the last century. The novel basically encompasses all political movements in the second half of the twentieth century, describes more than two hundred named characters and a considerable number of nameless but vivid characters, and lets readers enjoy reading the folk customs, chess cards traditions, medical development, culture, and education as well as erotic sensuality. It is a huge project.

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Page Count

982

Publisher

Xlibris Corporation

Published Date

ISBN 10

1524599522

ISBN 13

9781524599522

Multiscale Methods for Fredholm Integral Equations

By: Zhongying Chen,Charles A. Micchelli,Yuesheng Xu

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Multiscale Methods for Fredholm Integral Equations

By: Zhongying Chen,Charles A. Micchelli,Yuesheng Xu

Presents the state of the art in the study of fast multiscale methods for solving these equations based on wavelets.

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Page Count

551

Publisher

Cambridge University Press

Published Date

ISBN 10

1107103479

ISBN 13

9781107103474

Wavelet Analysis and Applications

By: Tao Qian,Mang I. Vai,Yuesheng Xu

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Wavelet Analysis and Applications

By: Tao Qian,Mang I. Vai,Yuesheng Xu

This volume reflects the latest developments in the area of wavelet analysis and its applications. Since the cornerstone lecture of Yves Meyer presented at the ICM 1990 in Kyoto, to some extent, wavelet analysis has often been said to be mainly an applied area. However, a significant percentage of contributions now are connected to theoretical mathematical areas, and the concept of wavelets continuously stretches across various disciplines of mathematics. Key topics: Approximation and Fourier Analysis Construction of Wavelets and Frame Theory Fractal and Multifractal Theory Wavelets in Numerical Analysis Time-Frequency Analysis Adaptive Representation of Nonlinear and Non-stationary Signals Applications, particularly in image processing Through the broad spectrum, ranging from pure and applied mathematics to real applications, the book will be most useful for researchers, engineers and developers alike.

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Page Count

567

Publisher

Springer Science & Business Media

Published Date

ISBN 10

376437778X

ISBN 13

9783764377786

Generalized Mercer Kernels and Reproducing Kernel Banach Spaces

By: Yuesheng Xu,Qi Ye

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Generalized Mercer Kernels and Reproducing Kernel Banach Spaces

By: Yuesheng Xu,Qi Ye

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Solve jigsaw puzzle

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Page Count

134

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470435500

ISBN 13

9781470435509

Book's by Yuesheng Xu

Multiscale Methods for Fredholm Integral Equations

Multiscale Methods for Fredholm Integral Equations

Generalized Mercer Kernels and Reproducing Kernel Banach Spaces

Generalized Mercer Kernels and Reproducing Kernel Banach Spaces

Rainbow

Rainbow

Multiscale Methods for Fredholm Integral Equations

Multiscale Methods for Fredholm Integral Equations

Wavelet Analysis and Applications

Wavelet Analysis and Applications

Generalized Mercer Kernels and Reproducing Kernel Banach Spaces

Generalized Mercer Kernels and Reproducing Kernel Banach Spaces

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