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Elementary Functions: Algorithms and Implementation

Jean-Michel Muller

Second Edition.

Resumen/Descripción – provisto por la editorial

No disponible.

Palabras clave – provistas por la editorial

Theory of Computation; Computer System Implementation; Applications of Mathematics; Numeric Computing; Computational Science and Engineering; Mathematics of Computing

Disponibilidad
Institución detectada Año de publicación Navegá Descargá Solicitá
No detectada 2006 SpringerLink

Información

Tipo de recurso:

libros

ISBN impreso

978-0-8176-4372-0

ISBN electrónico

978-0-8176-4408-6

Editor responsable

Springer Nature

País de edición

Reino Unido

Fecha de publicación

Información sobre derechos de publicación

© Birkhäuser Boston 2006

Tabla de contenidos

Introduction

Jean-Michel Muller

Electron tomography is an imaging technique that provides 3D images of a specimen with nanometer scale resolution. The range of specimens that can be investigated with this technique is particularly wide, from large (500–1000 nm) unique variable structures such as whole cells to suspensions of thousands of small identical macromolecules (>200 kDa).When applied to cryofixed frozen-hydrated biological material, the technique is often referred to as cryotomography. In combination with automated low-dose data collection and advanced computational methods, such as molecular identification based on pattern recognition, cryotomography can be used to visualize the architecture of small cells and organelles and/or to map macromolecular structures in their cellular environment. The resolution that can be obtained with cryotomography depends on several fundamental and technical issues related to specimen preparation, microscopy and subsequent image processing steps, but will typically be in the range of 5–10 nm.

- Introduction | Pp. 1-7

Some Basic Things About Computer Arithmetic

Jean-Michel Muller

Electron tomography is an imaging technique that provides 3D images of a specimen with nanometer scale resolution. The range of specimens that can be investigated with this technique is particularly wide, from large (500–1000 nm) unique variable structures such as whole cells to suspensions of thousands of small identical macromolecules (>200 kDa).When applied to cryofixed frozen-hydrated biological material, the technique is often referred to as cryotomography. In combination with automated low-dose data collection and advanced computational methods, such as molecular identification based on pattern recognition, cryotomography can be used to visualize the architecture of small cells and organelles and/or to map macromolecular structures in their cellular environment. The resolution that can be obtained with cryotomography depends on several fundamental and technical issues related to specimen preparation, microscopy and subsequent image processing steps, but will typically be in the range of 5–10 nm.

- Some Basic Things About Computer Arithmetic | Pp. 9-24

Polynomial or Rational Approximations

Jean-Michel Muller

Electron tomography is an imaging technique that provides 3D images of a specimen with nanometer scale resolution. The range of specimens that can be investigated with this technique is particularly wide, from large (500–1000 nm) unique variable structures such as whole cells to suspensions of thousands of small identical macromolecules (>200 kDa).When applied to cryofixed frozen-hydrated biological material, the technique is often referred to as cryotomography. In combination with automated low-dose data collection and advanced computational methods, such as molecular identification based on pattern recognition, cryotomography can be used to visualize the architecture of small cells and organelles and/or to map macromolecular structures in their cellular environment. The resolution that can be obtained with cryotomography depends on several fundamental and technical issues related to specimen preparation, microscopy and subsequent image processing steps, but will typically be in the range of 5–10 nm.

Part I - Algorithms Based on Polynomial Approximation and/or Table Lookup, Multiple-Precision Evaluation of Functions | Pp. 27-66

Table-Based Methods

Jean-Michel Muller

Electron tomography is an imaging technique that provides 3D images of a specimen with nanometer scale resolution. The range of specimens that can be investigated with this technique is particularly wide, from large (500–1000 nm) unique variable structures such as whole cells to suspensions of thousands of small identical macromolecules (>200 kDa).When applied to cryofixed frozen-hydrated biological material, the technique is often referred to as cryotomography. In combination with automated low-dose data collection and advanced computational methods, such as molecular identification based on pattern recognition, cryotomography can be used to visualize the architecture of small cells and organelles and/or to map macromolecular structures in their cellular environment. The resolution that can be obtained with cryotomography depends on several fundamental and technical issues related to specimen preparation, microscopy and subsequent image processing steps, but will typically be in the range of 5–10 nm.

Part I - Algorithms Based on Polynomial Approximation and/or Table Lookup, Multiple-Precision Evaluation of Functions | Pp. 67-87

Multiple-Precision Evaluation of Functions

Jean-Michel Muller

Electron tomography is an imaging technique that provides 3D images of a specimen with nanometer scale resolution. The range of specimens that can be investigated with this technique is particularly wide, from large (500–1000 nm) unique variable structures such as whole cells to suspensions of thousands of small identical macromolecules (>200 kDa).When applied to cryofixed frozen-hydrated biological material, the technique is often referred to as cryotomography. In combination with automated low-dose data collection and advanced computational methods, such as molecular identification based on pattern recognition, cryotomography can be used to visualize the architecture of small cells and organelles and/or to map macromolecular structures in their cellular environment. The resolution that can be obtained with cryotomography depends on several fundamental and technical issues related to specimen preparation, microscopy and subsequent image processing steps, but will typically be in the range of 5–10 nm.

Part I - Algorithms Based on Polynomial Approximation and/or Table Lookup, Multiple-Precision Evaluation of Functions | Pp. 89-100

Introduction to Shift-and-Add Algorithms

Jean-Michel Muller

Electron tomography is an imaging technique that provides 3D images of a specimen with nanometer scale resolution. The range of specimens that can be investigated with this technique is particularly wide, from large (500–1000 nm) unique variable structures such as whole cells to suspensions of thousands of small identical macromolecules (>200 kDa).When applied to cryofixed frozen-hydrated biological material, the technique is often referred to as cryotomography. In combination with automated low-dose data collection and advanced computational methods, such as molecular identification based on pattern recognition, cryotomography can be used to visualize the architecture of small cells and organelles and/or to map macromolecular structures in their cellular environment. The resolution that can be obtained with cryotomography depends on several fundamental and technical issues related to specimen preparation, microscopy and subsequent image processing steps, but will typically be in the range of 5–10 nm.

Part II - Shift-and-Add Algorithms | Pp. 103-131

The CORDIC Algorithm

Jean-Michel Muller

Electron tomography is an imaging technique that provides 3D images of a specimen with nanometer scale resolution. The range of specimens that can be investigated with this technique is particularly wide, from large (500–1000 nm) unique variable structures such as whole cells to suspensions of thousands of small identical macromolecules (>200 kDa).When applied to cryofixed frozen-hydrated biological material, the technique is often referred to as cryotomography. In combination with automated low-dose data collection and advanced computational methods, such as molecular identification based on pattern recognition, cryotomography can be used to visualize the architecture of small cells and organelles and/or to map macromolecular structures in their cellular environment. The resolution that can be obtained with cryotomography depends on several fundamental and technical issues related to specimen preparation, microscopy and subsequent image processing steps, but will typically be in the range of 5–10 nm.

Part II - Shift-and-Add Algorithms | Pp. 133-156

Some Other Shift-and-Add Algorithms

Jean-Michel Muller

Electron tomography is an imaging technique that provides 3D images of a specimen with nanometer scale resolution. The range of specimens that can be investigated with this technique is particularly wide, from large (500–1000 nm) unique variable structures such as whole cells to suspensions of thousands of small identical macromolecules (>200 kDa).When applied to cryofixed frozen-hydrated biological material, the technique is often referred to as cryotomography. In combination with automated low-dose data collection and advanced computational methods, such as molecular identification based on pattern recognition, cryotomography can be used to visualize the architecture of small cells and organelles and/or to map macromolecular structures in their cellular environment. The resolution that can be obtained with cryotomography depends on several fundamental and technical issues related to specimen preparation, microscopy and subsequent image processing steps, but will typically be in the range of 5–10 nm.

Part II - Shift-and-Add Algorithms | Pp. 157-169

Range Reduction

Jean-Michel Muller

Electron tomography is an imaging technique that provides 3D images of a specimen with nanometer scale resolution. The range of specimens that can be investigated with this technique is particularly wide, from large (500–1000 nm) unique variable structures such as whole cells to suspensions of thousands of small identical macromolecules (>200 kDa).When applied to cryofixed frozen-hydrated biological material, the technique is often referred to as cryotomography. In combination with automated low-dose data collection and advanced computational methods, such as molecular identification based on pattern recognition, cryotomography can be used to visualize the architecture of small cells and organelles and/or to map macromolecular structures in their cellular environment. The resolution that can be obtained with cryotomography depends on several fundamental and technical issues related to specimen preparation, microscopy and subsequent image processing steps, but will typically be in the range of 5–10 nm.

Part III - Range Reduction, Final Rounding and Exceptions | Pp. 173-191

Final Rounding

Jean-Michel Muller

Electron tomography is an imaging technique that provides 3D images of a specimen with nanometer scale resolution. The range of specimens that can be investigated with this technique is particularly wide, from large (500–1000 nm) unique variable structures such as whole cells to suspensions of thousands of small identical macromolecules (>200 kDa).When applied to cryofixed frozen-hydrated biological material, the technique is often referred to as cryotomography. In combination with automated low-dose data collection and advanced computational methods, such as molecular identification based on pattern recognition, cryotomography can be used to visualize the architecture of small cells and organelles and/or to map macromolecular structures in their cellular environment. The resolution that can be obtained with cryotomography depends on several fundamental and technical issues related to specimen preparation, microscopy and subsequent image processing steps, but will typically be in the range of 5–10 nm.

Part III - Range Reduction, Final Rounding and Exceptions | Pp. 193-216