{"id":"https://openalex.org/W2027178849","doi":"https://doi.org/10.1109/isccsp.2014.6877906","title":"The revised direct batch evaluation algorithm of optimal eigenvectors of the DFT matrix using the notion of Moore-Penrose matrix pseudoinverse","display_name":"The revised direct batch evaluation algorithm of optimal eigenvectors of the DFT matrix using the notion of Moore-Penrose matrix pseudoinverse","publication_year":2014,"publication_date":"2014-05-01","ids":{"openalex":"https://openalex.org/W2027178849","doi":"https://doi.org/10.1109/isccsp.2014.6877906","mag":"2027178849"},"language":"en","primary_location":{"id":"doi:10.1109/isccsp.2014.6877906","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isccsp.2014.6877906","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2014 6th International Symposium on Communications, Control and Signal Processing (ISCCSP)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069248573","display_name":"Magdy Tawfik Hanna","orcid":"https://orcid.org/0000-0001-5387-3073"},"institutions":[{"id":"https://openalex.org/I66513531","display_name":"Fayoum University","ror":"https://ror.org/023gzwx10","country_code":"EG","type":"education","lineage":["https://openalex.org/I66513531"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"Magdy Tawfik Hanna","raw_affiliation_strings":["Department of Engineering Mathematics and Physics, Fayoum University, Fayoum, Egypt","Dept. of Eng. Math. & Phys., Fayoum Univ., Fayoum, Egypt"],"affiliations":[{"raw_affiliation_string":"Department of Engineering Mathematics and Physics, Fayoum University, Fayoum, Egypt","institution_ids":["https://openalex.org/I66513531"]},{"raw_affiliation_string":"Dept. of Eng. Math. & Phys., Fayoum Univ., Fayoum, Egypt","institution_ids":["https://openalex.org/I66513531"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5069248573"],"corresponding_institution_ids":["https://openalex.org/I66513531"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.09649246,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":null,"issue":null,"first_page":"433","last_page":"436"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/moore\u2013penrose-pseudoinverse","display_name":"Moore\u2013Penrose pseudoinverse","score":0.7783550024032593},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.7716934680938721},{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.6913577318191528},{"id":"https://openalex.org/keywords/eigenvalue-algorithm","display_name":"Eigenvalue algorithm","score":0.6702296137809753},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6485484838485718},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6189563274383545},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5847135186195374},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5321022272109985},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5222038626670837},{"id":"https://openalex.org/keywords/defective-matrix","display_name":"Defective matrix","score":0.5101280808448792},{"id":"https://openalex.org/keywords/eigendecomposition-of-a-matrix","display_name":"Eigendecomposition of a matrix","score":0.49496859312057495},{"id":"https://openalex.org/keywords/generalized-eigenvector","display_name":"Generalized eigenvector","score":0.44530078768730164},{"id":"https://openalex.org/keywords/gaussian-elimination","display_name":"Gaussian elimination","score":0.43594539165496826},{"id":"https://openalex.org/keywords/qr-decomposition","display_name":"QR decomposition","score":0.41035011410713196},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40473559498786926},{"id":"https://openalex.org/keywords/diagonalizable-matrix","display_name":"Diagonalizable matrix","score":0.38548195362091064},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.36424362659454346},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35125434398651123},{"id":"https://openalex.org/keywords/matrix-function","display_name":"Matrix function","score":0.29297780990600586},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.27921125292778015},{"id":"https://openalex.org/keywords/state-transition-matrix","display_name":"State-transition matrix","score":0.1712481677532196},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.0899011492729187},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08158090710639954}],"concepts":[{"id":"https://openalex.org/C21556879","wikidata":"https://www.wikidata.org/wiki/Q43219517","display_name":"Moore\u2013Penrose pseudoinverse","level":3,"score":0.7783550024032593},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.7716934680938721},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.6913577318191528},{"id":"https://openalex.org/C109565186","wikidata":"https://www.wikidata.org/wiki/Q6766437","display_name":"Eigenvalue algorithm","level":5,"score":0.6702296137809753},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6485484838485718},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6189563274383545},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5847135186195374},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5321022272109985},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5222038626670837},{"id":"https://openalex.org/C36967811","wikidata":"https://www.wikidata.org/wiki/Q5251123","display_name":"Defective matrix","level":5,"score":0.5101280808448792},{"id":"https://openalex.org/C169756996","wikidata":"https://www.wikidata.org/wiki/Q194919","display_name":"Eigendecomposition of a matrix","level":3,"score":0.49496859312057495},{"id":"https://openalex.org/C147925508","wikidata":"https://www.wikidata.org/wiki/Q970767","display_name":"Generalized eigenvector","level":5,"score":0.44530078768730164},{"id":"https://openalex.org/C126312332","wikidata":"https://www.wikidata.org/wiki/Q2658","display_name":"Gaussian elimination","level":3,"score":0.43594539165496826},{"id":"https://openalex.org/C188060507","wikidata":"https://www.wikidata.org/wiki/Q653242","display_name":"QR decomposition","level":3,"score":0.41035011410713196},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40473559498786926},{"id":"https://openalex.org/C30072841","wikidata":"https://www.wikidata.org/wiki/Q1767080","display_name":"Diagonalizable matrix","level":4,"score":0.38548195362091064},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.36424362659454346},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35125434398651123},{"id":"https://openalex.org/C4263655","wikidata":"https://www.wikidata.org/wiki/Q2699958","display_name":"Matrix function","level":4,"score":0.29297780990600586},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.27921125292778015},{"id":"https://openalex.org/C22629506","wikidata":"https://www.wikidata.org/wiki/Q7602993","display_name":"State-transition matrix","level":4,"score":0.1712481677532196},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.0899011492729187},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08158090710639954},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isccsp.2014.6877906","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isccsp.2014.6877906","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2014 6th International Symposium on Communications, Control and Signal Processing (ISCCSP)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W606473257","https://openalex.org/W2045289624","https://openalex.org/W2075735090","https://openalex.org/W2090697566","https://openalex.org/W2116983948","https://openalex.org/W2156985745","https://openalex.org/W2164261333","https://openalex.org/W4301621763"],"related_works":["https://openalex.org/W2497112068","https://openalex.org/W2977088962","https://openalex.org/W3158528284","https://openalex.org/W2379841455","https://openalex.org/W2505322798","https://openalex.org/W2154250700","https://openalex.org/W2145005506","https://openalex.org/W2773391339","https://openalex.org/W114467503","https://openalex.org/W2027178849"],"abstract_inverted_index":{"The":[0,20,69],"problem":[1],"of":[2,5,13,53,56,66,82,96,100],"batch":[3],"generation":[4],"orthonormal":[6,64],"Hermite-Gaussian-like":[7],"eigenvectors":[8,35],"separately":[9],"for":[10,93],"each":[11],"eigenspace":[12],"the":[14,51,54,80,97,105,120,123],"DFT":[15],"matrix":[16,30,43,57,83,101,107,125],"F":[17,102],"is":[18,26,44],"reconsidered.":[19],"singular":[21],"value":[22],"decomposition":[23],"(SVD)":[24],"technique":[25,116],"applied":[27],"to":[28,46,61,89,113],"a":[29,114],"whose":[31],"columns":[32],"are":[33],"nonorthogonal":[34],"lying":[36],"in":[37,59],"one":[38],"eigenspace.":[39,68],"Moreover":[40],"this":[41],"key":[42,106,124],"allowed":[45],"be":[47],"rank-deficient":[48],"which":[49],"necessitates":[50],"adoption":[52],"notion":[55,81],"pseudoinverse":[58],"order":[60,98],"find":[62],"optimal":[63],"basis":[65],"that":[67,122],"contributed":[70],"Revised":[71],"Direct":[72],"Batch":[73],"Evaluation":[74],"by":[75],"constrained":[76],"Optimization":[77],"Algorithm":[78],"using":[79],"Pseudoinverse":[84],"(RDBEOAP)":[85],"has":[86,126],"been":[87],"shown":[88],"give":[90],"reasonable":[91],"results":[92],"large":[94],"values":[95],"N":[99],"-":[103,111],"where":[104],"becomes":[108],"rank":[109],"deficient":[110],"compared":[112],"similar":[115],"(RDBEOA)":[117],"based":[118],"on":[119],"assumption":[121],"full":[127],"rank.":[128]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
