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Automated DTM validation and progressive sampling algorithm of finite element array relaxation / Urho Rauhala in Photogrammetric Engineering & Remote Sensing, PERS, vol 55 n° 4 (april 1989)  

Public [article]  inPhotogrammetric Engineering & Remote Sensing, PERS > vol 55 n° 4 (april 1989) . - pp 449 - 465 Titre : Automated DTM validation and progressive sampling algorithm of finite element array relaxation Type de document : Article/Communication Auteurs : Urho Rauhala, Auteur ; D. Davis, Auteur ; K. Baker, Auteur Année de publication : 1989 Article en page(s) : pp 449 - 465 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Photogrammétrie numérique [Termes IGN] échantillonnage [Termes IGN] méthode des éléments finis [Termes IGN] modèle numérique de terrain [Termes IGN] photogrammétrie numérique Numéro de notice : A1989-077 Affiliation des auteurs : non IGN Thématique : IMAGERIE Nature : Article DOI : sans En ligne : https://www.asprs.org/wp-content/uploads/pers/1989journal/apr/1989_apr_449-465.p [...] Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=25037 [article]

Compiler positioning system : an array algebra formulation of digital photogrammetry / Urho Rauhala in Photogrammetric Engineering & Remote Sensing, PERS, vol 55 n° 3 (march 1989)  

Public [article]  inPhotogrammetric Engineering & Remote Sensing, PERS > vol 55 n° 3 (march 1989) . - pp 317 - 326 Titre : Compiler positioning system : an array algebra formulation of digital photogrammetry Type de document : Article/Communication Auteurs : Urho Rauhala, Auteur Année de publication : 1989 Article en page(s) : pp 317 - 326 Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Photogrammétrie numérique [Termes IGN] géopositionnement [Termes IGN] méthode des moindres carrés [Termes IGN] photogrammétrie numérique [Termes IGN] triangulation Numéro de notice : A1989-056 Affiliation des auteurs : non IGN Thématique : IMAGERIE Nature : Article DOI : sans En ligne : https://www.asprs.org/wp-content/uploads/pers/1989journal/mar/1989_mar_317-326.p [...] Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=25016 [article]

Calculation of loop inverses / Urho Rauhala (1976)

Public contenu dans [Two papers by Techn Dr Urho Rauhala] / Urho Rauhala (1976) Titre : Calculation of loop inverses Type de document : Article/Communication Auteurs : Urho Rauhala, Auteur Editeur : Stockholm : Royal Institute of Technology Année de publication : 1976 Collection : Fotogrammetriska meddelanden, ISSN 0071-8068 num. 2-38 Conférence : ASP 1975, Spring Convention Washington DC Washington DC - Etats-Unis Importance : pp 40 - 78 Format : 21 x 30 cm Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Analyse numérique [Termes IGN] algèbre linéaire [Termes IGN] calcul matriciel [Termes IGN] factorisation de Cholesky [Termes IGN] inverse généralisé [Termes IGN] tenseur Résumé : (auteur) The concept of loop inverses, originates from the interpolation technique using assumed grid observations as unknowns in the "calculus of matrix array', Rauhala (1972, 1972b). The theory of loop inverses was developed in the "array algebra" of Rauhala (1974) resulting in a unified and generalized theory of generalized matrix inverses. Array calculus use of Einstein's summation convention for array indices and the of so-called R-vectors and R-matrices in a more general way than is possible in the conventional vector, matrix end tensor algebras. Extremely large multidimensionaI and multisingular equation systems for grid observations may be effectively solved using array algebra and modern computers. Herein a brief presentation of some special loop inverses concerning mainly the combinations of 1- and m- inverses or the well known full rank least squares inverse of the element adjustment and the minimum norm -inverse of the condition adjustment is made. As an example the lm- inverses derived in more details and is seen to belong to the category of constrained inverse of Rao and Mitra (1971) but not necessarily to fill the definition of Bjerhammar (1955) for a g-inverse. As a special case the lm-inverse creates the Moore (1920) - Penrose (1955) pseudoinverse. The general loop inverses fill only the more general (weaker) condition YaY = Y instead of the more restricted condition AyA = A of the g—inverse. Some computational aspects and examples of applications of the le-inverse and pseudoinverse are given. An algorithm of "Array Cholesky" is deveIoped which a) allows singularities b) handles singular rectangular matrices as elements c) works directly on the observation equations without the intermediate stage of the building normal equations d) preserves the sparseness of the “not built” normal equations e) needs no intermediate inversion of the triangular hyper matrix in calculation of the solution and the weight coefficient matrix f) is suited to the solution of ill-conditioned systems by a priori choice and reordering of the most significant parameters g) is suited for array solutions. Outlines are drawn for the application of this method in the general simultaneous adjustment of photogrammetric and geodetic observations. Numéro de notice : C1976-003 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Communication Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=92981

A review of array algebra / Urho Rauhala (1976)

Public contenu dans [Two papers by Techn Dr Urho Rauhala] / Urho Rauhala (1976) Titre : A review of array algebra Type de document : Article/Communication Auteurs : Urho Rauhala, Auteur Editeur : Stockholm : Royal Institute of Technology Année de publication : 1976 Collection : Fotogrammetriska meddelanden, ISSN 0071-8068 num. 2-38 Conférence : ISP 1976, 13th international congress of photogrammetry ISP 11/07/1976 23/07/1976 Helsinki Finlande OA Proceedings Archives Importance : pp 1 - 130 Format : 21 x 30 cm Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Analyse numérique [Termes IGN] algèbre linéaire [Termes IGN] calcul matriciel [Termes IGN] calcul tensoriel [Termes IGN] covariance [Termes IGN] inverse généralisé Résumé : (auteur) Array Algebra is a concept generalizing conventional vector, matrix and tensor algebra. It deals with systems of multilinear equations that are at the base of the "fast" solution algorithms like the FFT. An array solution of N = ni parameters takes inN operations. Esti-mation using array algebra is based on the theory of loop inverses, which is an extension of the generalized matrix inverses. It compares, clarifies and generalizes the statistical concepts (u.e., BLUE, BLMBE, etc.) as defined by Rao. A multilinear function theory, the array prediction using covariance functions, is the main application of the array estimation. It includes Moritz's collocation, Wiener-Hopf prediction, Hardy's multiquadric functions and multilinear polynomials as special cases. It is based on banded R-matrices. With it, a solution of N = ni parameters takes only i N operations. This means unbelievable savings in computation and core space requirements compared with the conventional case. For example, a solution of the bilinear array solution of N = 10002 = 106 parameters requires only ten (10) minutes computing time if one operation takes 30ps. Using the conventional technique, only N = 1000 parameters would already take N3 30ps 8.3 hours computing time, and the same storage space as the array solution of N=10002 parameters. Numéro de notice : C1976-002 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Communication Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=92979

[Two papers by Techn Dr Urho Rauhala] / Urho Rauhala (1976)

Public Titre : [Two papers by Techn Dr Urho Rauhala] Type de document : Article/Communication Auteurs : Urho Rauhala, Auteur Editeur : Stockholm : Royal Institute of Technology Année de publication : 1976 Collection : Fotogrammetriska meddelanden, ISSN 0071-8068 num. 2-38 Importance : 208 p. Format : 21 x 30 cm Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Analyse numérique Index. décimale : 23.40 Analyse numérique Numéro de notice : 25028 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Communication Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=92978

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• A review of array algebra / Urho Rauhala (1976)
• Calculation of loop inverses / Urho Rauhala (1976)

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Array algebra with applications in photogrammetry and geodesy / Urho Rauhala (1974)

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Calculus of matrix arrays and general polynomial and harmonic interpolation by least squares with new solutions in photogrammetry and geodesy / Urho Rauhala (1972)

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