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Download or read book Dense Subspaces in Hermitean Spaces of Uncountable Dimensions written by Mikko Saarimäki and published by . This book was released on 1983 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author: Quaintance Jocelyn
Publisher: World Scientific
Published: 2020-03-16
Total Pages: 896
ISBN-13: 9811216584
DOWNLOAD EBOOKVolume 2 applies the linear algebra concepts presented in Volume 1 to optimization problems which frequently occur throughout machine learning. This book blends theory with practice by not only carefully discussing the mathematical under pinnings of each optimization technique but by applying these techniques to linear programming, support vector machines (SVM), principal component analysis (PCA), and ridge regression. Volume 2 begins by discussing preliminary concepts of optimization theory such as metric spaces, derivatives, and the Lagrange multiplier technique for finding extrema of real valued functions. The focus then shifts to the special case of optimizing a linear function over a region determined by affine constraints, namely linear programming. Highlights include careful derivations and applications of the simplex algorithm, the dual-simplex algorithm, and the primal-dual algorithm. The theoretical heart of this book is the mathematically rigorous presentation of various nonlinear optimization methods, including but not limited to gradient decent, the Karush-Kuhn-Tucker (KKT) conditions, Lagrangian duality, alternating direction method of multipliers (ADMM), and the kernel method. These methods are carefully applied to hard margin SVM, soft margin SVM, kernel PCA, ridge regression, lasso regression, and elastic-net regression. Matlab programs implementing these methods are included.
Download or read book Linear Algebra And Optimization With Applications To Machine Learning - Volume Ii: Fundamentals Of Optimization Theory With Applications To Machine Learning written by Quaintance Jocelyn and published by World Scientific. This book was released on 2020-03-16 with total page 896 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 2 applies the linear algebra concepts presented in Volume 1 to optimization problems which frequently occur throughout machine learning. This book blends theory with practice by not only carefully discussing the mathematical under pinnings of each optimization technique but by applying these techniques to linear programming, support vector machines (SVM), principal component analysis (PCA), and ridge regression. Volume 2 begins by discussing preliminary concepts of optimization theory such as metric spaces, derivatives, and the Lagrange multiplier technique for finding extrema of real valued functions. The focus then shifts to the special case of optimizing a linear function over a region determined by affine constraints, namely linear programming. Highlights include careful derivations and applications of the simplex algorithm, the dual-simplex algorithm, and the primal-dual algorithm. The theoretical heart of this book is the mathematically rigorous presentation of various nonlinear optimization methods, including but not limited to gradient decent, the Karush-Kuhn-Tucker (KKT) conditions, Lagrangian duality, alternating direction method of multipliers (ADMM), and the kernel method. These methods are carefully applied to hard margin SVM, soft margin SVM, kernel PCA, ridge regression, lasso regression, and elastic-net regression. Matlab programs implementing these methods are included.
Author: Jean Gallier
Publisher: Springer Nature
Published: 2020-08-18
Total Pages: 627
ISBN-13: 3030460479
DOWNLOAD EBOOKThis textbook explores advanced topics in differential geometry, chosen for their particular relevance to modern geometry processing. Analytic and algebraic perspectives augment core topics, with the authors taking care to motivate each new concept. Whether working toward theoretical or applied questions, readers will appreciate this accessible exploration of the mathematical concepts behind many modern applications. Beginning with an in-depth study of tensors and differential forms, the authors go on to explore a selection of topics that showcase these tools. An analytic theme unites the early chapters, which cover distributions, integration on manifolds and Lie groups, spherical harmonics, and operators on Riemannian manifolds. An exploration of bundles follows, from definitions to connections and curvature in vector bundles, culminating in a glimpse of Pontrjagin and Chern classes. The final chapter on Clifford algebras and Clifford groups draws the book to an algebraic conclusion, which can be seen as a generalized viewpoint of the quaternions. Differential Geometry and Lie Groups: A Second Course captures the mathematical theory needed for advanced study in differential geometry with a view to furthering geometry processing capabilities. Suited to classroom use or independent study, the text will appeal to students and professionals alike. A first course in differential geometry is assumed; the authors’ companion volume Differential Geometry and Lie Groups: A Computational Perspective provides the ideal preparation.
Download or read book Differential Geometry and Lie Groups written by Jean Gallier and published by Springer Nature. This book was released on 2020-08-18 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook explores advanced topics in differential geometry, chosen for their particular relevance to modern geometry processing. Analytic and algebraic perspectives augment core topics, with the authors taking care to motivate each new concept. Whether working toward theoretical or applied questions, readers will appreciate this accessible exploration of the mathematical concepts behind many modern applications. Beginning with an in-depth study of tensors and differential forms, the authors go on to explore a selection of topics that showcase these tools. An analytic theme unites the early chapters, which cover distributions, integration on manifolds and Lie groups, spherical harmonics, and operators on Riemannian manifolds. An exploration of bundles follows, from definitions to connections and curvature in vector bundles, culminating in a glimpse of Pontrjagin and Chern classes. The final chapter on Clifford algebras and Clifford groups draws the book to an algebraic conclusion, which can be seen as a generalized viewpoint of the quaternions. Differential Geometry and Lie Groups: A Second Course captures the mathematical theory needed for advanced study in differential geometry with a view to furthering geometry processing capabilities. Suited to classroom use or independent study, the text will appeal to students and professionals alike. A first course in differential geometry is assumed; the authors’ companion volume Differential Geometry and Lie Groups: A Computational Perspective provides the ideal preparation.
Download or read book Shape Optimization and Unilateral Boundary Value Problems written by Timo Tiihonen and published by . This book was released on 1987 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author: Jyväskylän yliopisto. Matematiikan laitos
Publisher:
Published: 1987
Total Pages: 358
ISBN-13:
DOWNLOAD EBOOKDownload or read book Bericht written by Jyväskylän yliopisto. Matematiikan laitos and published by . This book was released on 1987 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book F-harmonic Measure in a Non-linear Potential Theory written by Juha Heinonen and published by . This book was released on 1986 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proceedings of the Summer School in Numerical Analysis at Jyväskylä written by Pekka Neittaanmäki and published by . This book was released on 1985 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Compatibility of the Initial and Boundary Values in Quasi-parabolic Problems written by Veikko T. Purmonen and published by . This book was released on 1986 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sensitivity Analysis for a Class of Optimal Shape Design Problems written by Pekka Neittaanmäki and published by . This book was released on 1985 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 804 pages. Available in PDF, EPUB and Kindle. Book excerpt:
