Algebraic geodesy and geoinformatics:
Gespeichert in:
| Format: | Medienkombination Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Heidelberg [u.a.]
Springer
2010
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XVIII, 377 S. graph. Darst. 235 mm x 155 mm 1 CD-ROM (12 cm) |
| ISBN: | 9783642121234 |
Internformat
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| 245 | 1 | 0 | |a Algebraic geodesy and geoinformatics |c Joseph L. Awange ... |
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Datensatz im Suchindex
| _version_ | 1805093749528723456 |
|---|---|
| adam_text |
4-4 CONCLUDING REMARKS 47 CONTENTS 1 INTRODUCTION 1 1-1 MOTIVATION 1 1-2
MODERN CHALLENGES 1 1-3 FACING THE CHALLENGES 2 1-4 CONCLUDING REMARKS 5
PART I ALGEBRAIC SYMBOLIC AND NUMERIC METHODS 2 BASICS OF RING THEORY 9
2-1 SOME APPLICATIONS TO GEODESY AND GEOINFORMATICS 9 2-2 NUMBERS FROM
OPERATIONAL PERSPECTIVE 9 2-3 NUMBER RINGS 13 2-4 CONCLUDING REMARKS 16
3 BASICS OF POLYNOMIAL THEORY 17 3-1 POLYNOMIAL EQUATIONS 17 3-2
POLYNOMIAL RINGS 18 3-21 POLYNOMIAL OBJECTS AS RINGS 18 3-22 OPERATIONS
"ADDITION" AND "MULTIPLICATION" 20 3-3 FACTORING POLYNOMIALS 21 3-4
POLYNOMIAL ROOTS 21 3-5 MINIMAL POLYNOMIALS 22 3-6 UNIVARIATE
POLYNOMIALS WITH REAL COEFFICIENTS 23 3-61 QUADRATIC POLYNOMIALS 23 3-62
CUBIC POLYNOMIALS 25 3-63 QUARTIC POLYNOMIALS 26 3-7 METHODS FOR
INVESTIGATING ROOTS 27 3-71 LOGARITHMIC AND CONTOUR PLOTS ON COMPLEX
PLANE 27 3-72 ISOGRAPH SIMULATOR 29 3-73 APPLICATION OF INVERSE SERIES
29 3-8 COMPUTATION OF ZEROS OF POLYNOMIAL SYSTEMS 30 3-9 CONCLUDING
REMARKS 32 4 GROEBNER BASIS 33 4-1 THE ORIGIN 33 4-2 BASICS OF GROEBNER
BASIS 34 4-3 BUCHBERGER ALGORITHM 40 4-31 MATHEMATICA COMPUTATION OF
GROEBNER BASIS 45 4-32 MAPLE COMPUTATION OF GROEBNER BASIS 46
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1000389065 DIGITALISIERT
DURCH XIV CONTENTS 5 POLYNOMIAL RESULTANTS 49 5-1 RESULTANTS: AN
ALTERNATIVE TO GROEBNER BASIS 49 5-2 SYLVESTER RESULTANTS 49 5-3
MULTIPOLYNOMIAL RESULTANTS 51 5-31 F. MACAULAY FORMULATION: 52 5-32 B.
STURMFELS' FORMULATION 54 5-33 THE DIXON RESULTANT 55 5-331 BASIC
CONCEPTS 55 5-332 FORMULATION OF THE DIXON RESULTANT 56 5-333 DIXON'S
GENERALIZATION OF THE CAYLEY-BEZOUT METHOD 57 5-334 IMPROVED DIXON
RESULTANT - KAPUR-SAXENA-YANG METHOD 58 5-335 HEURISTIC METHODS TO
ACCELERATE THE DIXON RESULTANT 59 5-336 EARLY DISCOVERY OF FACTORS: THE
EDF METHOD 60 5-4 CONCLUDING REMARKS 61 6 LINEAR HOMOTPY 63 6-1
INTRODUCTORY REMARKS 63 6-2 BACKGROUND TO HOMOTOPY 63 6-3 DEFINITION AND
BASIC CONCEPTS 64 6-4 SOLVING NONLINEAR EQUATIONS VIA HOMOTOPY 65 6-41
TRACING HOMOTOPY PATH AS INITIAL VALUE PROBLEM 69 6-42 TYPES OF LINEAR
HOMOTOPY 71 6-421 FIXED POINT HOMOTOPY 71 6-422 NEWTON HOMOTOPY 71 6-423
START SYSTEM FOR POLYNOMIAL SYSTEMS 72 6-5 CONCLUDING REMARKS 76 7
SOLUTIONS OF OVERDETERMINED SYSTEMS 79 7-1 ESTIMATING GEODETIC AND
GEOINFORMATICS UNKNOWNS 79 7-2 ALGEBRAIC LEAST SQUARE SOLUTION (ALESS)
80 7-21 TRANSFORMING OVERDETERMINED SYSTEMS TO DETERMINED 80 7-22
SOLVING THE DETERMINED SYSTEM 82 7-3 GAUSS-JACOBI COMBINATORIAL
ALGORITHM 84 7-3 CONTENTS XV EXTENDED NEWTON-RAPHSON METHOD 101 8-1
INTRODUCTORY REMARKS 101 8-2 THE STANDARD NEWTON-RAPHSON APPROACH 102
8-3 EXAMPLES OF LIMITATIONS OF THE STANDARD APPROACH 102 8-31
OVERDETERMINED POLYNOMIAL SYSTEMS 102 8-32 OVERDETERMINED NON-POLYNOMIAL
SYSTEM 104 8-33 DETERMINED POLYNOMIAL SYSTEM 105 8-34 UNDERDETERMINED
POLYNOMIAL SYSTEM 106 8-4 EXTENDING THE NEWTON-RAPHSON APPROACH USING
PSEUDOINVERSE . 107 8-5 APPLICATIONS OF THE EXTENDED NEWTON-RAPHSON
METHOD 108 8-6 CONCLUDING REMARKS 110 PROCRUSTES SOLUTION ILL 9-1
MOTIVATION ILL 9-2 PROCRUSTES: ORIGIN AND APPLICATIONS 112 9-21
PROCRUSTES AND THE MAGIC BED 112 9-22 MULTIDIMENSIONAL SCALING 114 9-23
APPLICATIONS OF PROCRUSTES IN MEDICINE 114 9-231 GENE RECOGNITION 114
9-232 IDENTIFICATION OF MALARIA PARASITES 115 9-3 PARTIAL PROCRUSTES
SOLUTION 116 9-31 CONVENTIONAL FORMULATION 116 9-32 PARTIAL DERIVATIVE
FORMULATION 118 9-4 THE GENERAL PROCRUSTES SOLUTION 119 9-5 EXTENDED
GENERAL PROCRUSTES SOLUTION 130 9-51 MILD ANISOTROPY IN SCALING 130 9-52
STRONG ANISOTROPY IN SCALLING 131 9-6 WEIGHTED PROCRUSTES TRANSFORMATION
133 9-7 CONCLUDING REMARKS 135 PART II APPLICATIONS TO GEODESY AND
GEOINFORMATICS 10 LPS-GNSS ORIENTATIONS AND VERTICAL DEFLECTIONS 139
10-1 INTRODUCTORY REMARKS 139 10- XVI CONTENTS 11 CARTESIAN TO
ELLIPSOIDAL MAPPING 155 11-1 INTRODUCTORY REMARKS 155 11-2 MAPPING
TOPOGRAPHICAL POINTS ONTO REFERENCE ELLIPSOID 155 11-3 MAPPING GEOMETRY
158 11-4 MINIMUM DISTANCE MAPPING 160 11-41 GRAFAREND-LOHSE'S MAPPING OF
T 2 * E 2AAB 163 11-42 GROEBNER BASIS' MAPPING OF T 2 * Y E 2 A 6 164
11-43 EXTENDED NEWTON-RAPHSON'S MAPPING OF T 2 * * E 2 AB 166 11-5
CONCLUDING REMARKS 171 12 POSITIONING BY RANGING 173 12-1 APPLICATIONS
OF DISTANCES 173 12-2 RANGING BY GLOBAL NAVIGATION SATELLITE SYSTEM
(GNSS) 174 12-21 THE PSEUDO-RANGING FOUR-POINTS PROBLEM 174 12-211
STURMFELS' APPROACH 177 12-212 GROEBNER BASIS APPROACH 179 12-22 RANGING
TO MORE THAN FOUR GPS SATELLITES 181 12-221 EXTENDED NEWTON-RAPHSON
SOLUTION 185 12-222 HOMOTOPY SOLUTION OF GPS N-POINT PROBLEM 187 12-223
LEAST SQUARES VERSUS GAUSS-JACOBI COMBINATORIAL. 189 12-3 RANGING BY
LOCAL POSITIONING SYSTEMS (LPS) 191 12-31 PLANAR RANGING 192 12-311
CONVENTIONAL APPROACH 192 12-312 SYLVESTER RESULTANTS APPROACH 193
12-313 REDUCED GROEBNER BASIS APPROACH 194 12-31 CONTENTS XVII 13-213
STURMFELS' RESULTANT APPROACH 223 13-22 THREE-DIMENSIONAL RESECTION 226
13-221 EXACT SOLUTION 226 13-222 SOLUTION OF GRUNERT'S DISTANCE
EQUATIONS 226 13-223 GROEBNER BASIS SOLUTION OF GRUNERT'S EQUATIONS .
228 13-224 POLYNOMIAL RESULTANTS' SOLUTION OF GRUNERT'S DISTANCE
EQUATIONS 230 13-225 LINEAR HOMOTOPY SOLUTION 233 13-226
GRAFAREND-LOHSE-SCHAFFRIN APPROACH 237 13-227 3D-RESECTION TO MORE THAN
THREE KNOWN STATIONS . 240 13-3 PHOTOGRAMMETRIC RESECTION 244 13-31
GRAFAREND-SHAN MOEBIUS PHOTOGRAMMETRIC RESECTION 245 13-32 ALGEBRAIC
PHOTOGRAMMETRIC RESECTION 246 13-4 CONCLUDING REMARKS 248 14 POSITIONING
BY INTERSECTION METHODS 249 14-1 INTERSECTION PROBLEM AND ITS IMPORTANCE
249 14-2 GEODETIC INTERSECTION 250 14-21 PLANAR INTERSECTION 250 14-211
CONVENTIONAL SOLUTION 250 14-212 REDUCED GROEBNER BASIS SOLUTION 251
14-22 THREE-DIMENSIONAL INTERSECTION 254 14-221 CLOSED FORM SOLUTION 254
14-222 CONVENTIONAL SOLUTION 255 14-223 REDUCED GROEBNER BASIS SOLUTION
255 14-224 STURMFELS' RESULTANTS SOLUTION 256 14-225 INTERSECTION TO
MORE THAN THREE KNOWN STATIONS . 259 14-3 PHOTOGRAMMETRIC
INTERSECTION 261 14-306 GRAFAREND-SHAN MOEBIUS APPROACH 262 14-307
COMMUTATIVE ALGEBRAIC APPROACHES 263 14-4 CONCLUDING REMARKS 263 15 GNSS
ENVIRONMENTAL MONITORING 265 15- XVIII CONTENTS 16 ALGEBRAIC DIAGNOSIS
OF OUTLIERS 289 16-1 OUTLIERS IN OBSERVATION SAMPLES 289 16-2 ALGEBRAIC
DIAGNOSIS OF OUTLIERS 290 16-21 OUTLIER DIAGNOSIS IN PLANAR RANGING 292
16-22 DIAGNOSIS OF MULTIPATH ERROR IN GNSS POSITIONING 296 16-3
CONCLUDING REMARKS 300 17 DATUM TRANSFORMATION PROBLEMS 303 17-1 THE
7-PARAMETER DATUM TRANSFORMATION AND ITS IMPORTANCE 303 17-2 ALGEBRAIC
SOLUTION OF THE 7-PARAMETER TRANSFORMATION PROBLEM 305 17-21 GROEBNER
BASIS TRANSFORMATION 305 17-22 DIXON RESULTANT SOLUTION 309 17-23
GAUSS-JACOBI COMBINATORIAL TRANSFORMATION 313 17-3 THE 9-PARAMETER
(AFFINE) DATUM TRANSFORMATION 318 17-4 ALGEBRAIC SOLUTION OF THE
9-PARAMETER TRANSFORMATION 320 17-41 THE 3-POINT AFFINE TRANSFORMATION
PROBLEM 320 17-411 SIMPLIFICATIONS FOR THE SYMBOLIC SOLUTION 320 17-412
SYMBOLIC SOLUTION WITH DIXON RESULTANT 321 17-413 SYMBOLIC SOLUTION WITH
REDUCED GROEBNER BASIS . 323 17-42 THE N-POINTS PROBLEM 325 17-421
ALESS APPROACH TO OVERDETERMINED CASES 327 17-422 HOMOTOPY SOLUTION OF
THE ALESS-DETERMINED MODEL 329 17-43 PROCRUSTES SOLUTION 333 17-5
CONCLUDING REMARK 337 APPENDIX 339 APPENDIX A-L: DEFINITIONS 339
APPENDIX A-2: C. F. GAUSS COMBINATORIAL APPROACH 340 APPENDIX A-3:
LINEAR HOMOTOPY 343 APPENDIX A-4: DETERMINED SYSTEM OF THE 9-PARAMETER
TRANSFORMATION N |
| any_adam_object | 1 |
| author_GND | (DE-588)123537959 |
| building | Verbundindex |
| bvnumber | BV036105755 |
| classification_rvk | RB 10103 RB 10104 RB 10109 SK 950 SK 990 |
| ctrlnum | (OCoLC)634313069 (DE-599)DNB1000389065 |
| dewey-full | 526 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 526 - Mathematical geography |
| dewey-raw | 526 |
| dewey-search | 526 |
| dewey-sort | 3526 |
| dewey-tens | 520 - Astronomy and allied sciences |
| discipline | Physik Geologie / Paläontologie Mathematik Geographie |
| edition | 2. ed. |
| format | Kit Book |
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| indexdate | 2024-07-20T10:32:27Z |
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| isbn | 9783642121234 |
| language | English |
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| spellingShingle | Algebraic geodesy and geoinformatics GPS (DE-588)4216824-7 gnd Geodäsie (DE-588)4020202-1 gnd Berechnung (DE-588)4120997-7 gnd Geoinformatik (DE-588)7571300-7 gnd Geoinformationssystem (DE-588)4261642-6 gnd Computeralgebra (DE-588)4010449-7 gnd |
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| title | Algebraic geodesy and geoinformatics |
| title_auth | Algebraic geodesy and geoinformatics |
| title_exact_search | Algebraic geodesy and geoinformatics |
| title_full | Algebraic geodesy and geoinformatics Joseph L. Awange ... |
| title_fullStr | Algebraic geodesy and geoinformatics Joseph L. Awange ... |
| title_full_unstemmed | Algebraic geodesy and geoinformatics Joseph L. Awange ... |
| title_short | Algebraic geodesy and geoinformatics |
| title_sort | algebraic geodesy and geoinformatics |
| topic | GPS (DE-588)4216824-7 gnd Geodäsie (DE-588)4020202-1 gnd Berechnung (DE-588)4120997-7 gnd Geoinformatik (DE-588)7571300-7 gnd Geoinformationssystem (DE-588)4261642-6 gnd Computeralgebra (DE-588)4010449-7 gnd |
| topic_facet | GPS Geodäsie Berechnung Geoinformatik Geoinformationssystem Computeralgebra |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3430802&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018996025&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT awangejosephl algebraicgeodesyandgeoinformatics |