Algorithms for the Solution of the Nonlinear Least-Squares Problem
This paper describes a modification to the Gauss-Newton method for the solution of nonlinear least-squares problems. The new method seeks to avoid the deficiencies in the Gauss-Newton method by improving, when necessary, the Hessian approximation by specifically including or approximating some of th...
Saved in:
| Published in | SIAM journal on numerical analysis Vol. 15; no. 5; pp. 977 - 992 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Philadelphia
Society for Industrial and Applied Mathematics
01.10.1978
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 0036-1429 1095-7170 |
| DOI | 10.1137/0715063 |
Cover
| Abstract | This paper describes a modification to the Gauss-Newton method for the solution of nonlinear least-squares problems. The new method seeks to avoid the deficiencies in the Gauss-Newton method by improving, when necessary, the Hessian approximation by specifically including or approximating some of the neglected terms. The method seeks to compute the search direction without the need to form explicitly either the Hessian approximation or a factorization of this matrix. The benefits of this are similar to that of avoiding the formation of the normal equations in the Gauss-Newton method. Three algorithms based on this method are described: one which assumes that second derivative information is available and two which only assume first derivatives can be computed. |
|---|---|
| AbstractList | This paper describes a modification to the Gauss-Newton method for the solution of nonlinear least-squares problems. The new method seeks to avoid the deficiencies in the Gauss-Newton method by improving, when necessary, the Hessian approximation by specifically including or approximating some of the neglected terms. The method seeks to compute the search direction without the need to form explicitly either the Hessian approximation or a factorization of this matrix. The benefits of this are similar to that of avoiding the formation of the normal equations in the Gauss-Newton method. Three algorithms based on this method are described: one which assumes that second derivative information is available and two which only assume first derivatives can be computed. |
| Author | Gill, Philip E. Murray, Walter |
| Author_xml | – sequence: 1 givenname: Philip E. surname: Gill fullname: Gill, Philip E. – sequence: 2 givenname: Walter surname: Murray fullname: Murray, Walter |
| BookMark | eNpt0M9LwzAUB_AgCm5T_Ac8FC-eonlNmqbHOfwFQ4XpuaTpi-vomi1JD_73dm54EE-PL3x4j_cdk-POdUjIBbAbAJ7fshwyJvkRGQErMppDzo7JiDEuKYi0OCXjEFZsyAr4iNxN20_nm7hch8Q6n8QlJgvX9rFxXeLsT35xXdt0qH0yRx0iXWx77TEkb95VLa7PyInVbcDzw5yQj4f799kTnb8-Ps-mc2pACUU1K5QsqhSEzEBVyOvMoqlZlXOsbaVtKpSptREirYc_lEbDKs5AAx8oCj4hV_u9G--2PYZYrlzvu-FkWaRcpkwVakB0j4x3IXi0pWmi3n0TvW7aEli5a6k8tDT46z9-45u19l__yMu9XIXo_C9LIZM5SP4NqLpwXg |
| CitedBy_id | crossref_primary_10_1016_0098_1354_93_80086_3 crossref_primary_10_1177_1475921719834045 crossref_primary_10_1088_0022_3727_23_12_003 crossref_primary_10_1016_0584_8539_90_80040_6 crossref_primary_10_1016_0006_2952_91_90074_F crossref_primary_10_3168_jds_2008_1361 crossref_primary_10_1080_00207728808964043 crossref_primary_10_1016_j_asr_2020_06_004 crossref_primary_10_1186_BF03546533 crossref_primary_10_1016_j_comnet_2008_11_004 crossref_primary_10_1016_j_eti_2019_100456 crossref_primary_10_1007_s00254_008_1619_z crossref_primary_10_1016_S1874_1029_13_60036_1 crossref_primary_10_20537_2076_7633_2015_7_1_159_176 crossref_primary_10_1016_j_isprsjprs_2017_05_008 crossref_primary_10_1016_j_ymssp_2014_11_001 crossref_primary_10_1016_j_neuroimage_2014_08_049 crossref_primary_10_3905_jod_2011_18_3_007 crossref_primary_10_1016_j_cplett_2015_02_002 crossref_primary_10_1080_10682760310001598698 crossref_primary_10_1016_j_corsci_2008_03_015 crossref_primary_10_1016_0360_1323_93_90046_6 crossref_primary_10_1016_j_corsci_2013_03_036 crossref_primary_10_3390_s20030639 crossref_primary_10_1016_S0021_9258_19_37589_1 crossref_primary_10_1097_RLI_0000000000000094 crossref_primary_10_1109_TIP_2010_2052274 crossref_primary_10_1109_78_134483 crossref_primary_10_1002_aic_14861 crossref_primary_10_1109_59_192977 crossref_primary_10_1002_mrm_1910390222 crossref_primary_10_1016_j_jorganchem_2006_12_019 crossref_primary_10_1007_BF00127817 crossref_primary_10_1109_ACCESS_2021_3073670 crossref_primary_10_1016_j_cherd_2010_11_021 crossref_primary_10_1016_j_compag_2016_08_003 crossref_primary_10_1016_j_jhazmat_2008_01_052 crossref_primary_10_1007_BF00964956 crossref_primary_10_1103_PhysRevLett_104_060201 crossref_primary_10_1016_S0009_3084_96_02626_6 crossref_primary_10_1016_j_fluid_2013_08_039 crossref_primary_10_1051_0004_6361_200912485 crossref_primary_10_1063_1_4922186 crossref_primary_10_1016_j_eswa_2016_02_026 crossref_primary_10_3390_rs13152975 crossref_primary_10_1016_j_enbuild_2016_11_022 crossref_primary_10_1002_nbm_1601 crossref_primary_10_1109_TSP_2011_2161302 crossref_primary_10_4236_msa_2019_912066 crossref_primary_10_1007_s11356_014_3174_3 crossref_primary_10_1590_2358_2936e2021012 crossref_primary_10_1016_j_cam_2003_08_052 crossref_primary_10_1093_jee_tox233 crossref_primary_10_1007_BF02798423 crossref_primary_10_1364_BOE_495489 crossref_primary_10_1016_j_jmapro_2023_05_075 crossref_primary_10_1007_s41660_023_00312_3 crossref_primary_10_1016_0165_1684_89_90021_2 crossref_primary_10_1051_0004_6361_200912133 crossref_primary_10_1002_2013JE004580 crossref_primary_10_1111_j_1365_2672_1983_tb02653_x crossref_primary_10_1021_jp048440q crossref_primary_10_1109_TITS_2012_2187896 crossref_primary_10_2528_PIERB14072907 crossref_primary_10_1007_s00410_007_0187_7 crossref_primary_10_1080_00207160_2012_736617 crossref_primary_10_1016_j_apm_2017_05_009 crossref_primary_10_1364_AO_54_009889 crossref_primary_10_1016_j_corsci_2010_09_016 crossref_primary_10_1364_AO_50_002679 crossref_primary_10_3390_rs14092055 crossref_primary_10_1007_s00498_023_00361_6 crossref_primary_10_1016_0013_4686_92_85010_I crossref_primary_10_1016_0142_0615_87_90032_9 crossref_primary_10_1016_j_corsci_2013_06_030 crossref_primary_10_1016_j_ijthermalsci_2022_107549 crossref_primary_10_1155_2016_4041827 crossref_primary_10_1016_S0262_8856_97_00010_3 crossref_primary_10_1109_TCST_2013_2260545 crossref_primary_10_1109_TIE_2013_2257142 crossref_primary_10_1016_0885_4505_87_90096_X crossref_primary_10_1063_1_1143846 crossref_primary_10_1063_1_3456171 crossref_primary_10_1002_zamm_19950750505 crossref_primary_10_1016_j_isprsjprs_2024_09_014 crossref_primary_10_1063_1_1935516 crossref_primary_10_1243_PIME_PROC_1988_202_045_02 crossref_primary_10_1006_abbi_2001_2317 crossref_primary_10_1080_14697688_2019_1633014 crossref_primary_10_1109_TPS_2024_3519032 crossref_primary_10_1115_1_4048811 crossref_primary_10_1016_0022_4073_93_90072_P crossref_primary_10_1109_TRO_2008_2006866 crossref_primary_10_1017_S0025315409000010 crossref_primary_10_1016_j_corsci_2014_10_012 crossref_primary_10_1177_004051759106101208 crossref_primary_10_1080_01630563_2015_1046080 crossref_primary_10_1111_aogs_14791 crossref_primary_10_1109_TVT_2017_2742665 crossref_primary_10_1021_ac5019952 crossref_primary_10_1088_0022_3735_18_5_014 crossref_primary_10_1177_004051759306300704 crossref_primary_10_1021_ac202726n crossref_primary_10_1007_s10800_016_1042_1 crossref_primary_10_1016_j_sigpro_2008_01_015 crossref_primary_10_1039_b514563p crossref_primary_10_1080_00207160_2019_1578348 crossref_primary_10_1006_cviu_1999_0832 crossref_primary_10_1016_j_cej_2022_139125 crossref_primary_10_1029_2018JE005580 crossref_primary_10_1111_cgf_13024 crossref_primary_10_1016_0038_1101_92_90016_6 crossref_primary_10_1029_92JC02122 crossref_primary_10_1007_s10589_016_9829_x crossref_primary_10_1134_S1024856011050137 crossref_primary_10_1016_j_jbiomech_2024_112175 crossref_primary_10_1016_j_apnum_2018_11_008 crossref_primary_10_1016_S0021_9258_18_60954_8 crossref_primary_10_1016_0740_0020_84_90005_4 crossref_primary_10_1016_j_spmi_2014_10_024 crossref_primary_10_3390_rs16193547 crossref_primary_10_1016_j_tca_2009_03_001 crossref_primary_10_3390_math9141695 crossref_primary_10_1109_10_19855 crossref_primary_10_1016_0735_1933_91_90080_N crossref_primary_10_1002__SICI_1520_6548_199906_14_5_401__AID_GEA3_3_0_CO_2_A crossref_primary_10_1088_0022_3727_40_17_053 crossref_primary_10_1007_s11265_012_0717_z crossref_primary_10_3847_1538_3881_aba836 crossref_primary_10_1016_j_electacta_2013_10_099 crossref_primary_10_1016_j_rse_2019_01_019 crossref_primary_10_1021_ac4022105 crossref_primary_10_1061__ASCE_EE_1943_7870_0000335 crossref_primary_10_14358_PERS_76_4_439 crossref_primary_10_1007_s00521_012_0866_9 crossref_primary_10_1140_epjst_e2008_00455_y crossref_primary_10_1080_07313569408955589 crossref_primary_10_1080_03052150008940918 crossref_primary_10_1080_18756891_2008_9727630 crossref_primary_10_1177_009286159603000206 crossref_primary_10_1109_JSEN_2016_2585438 crossref_primary_10_1080_00268970500044764 crossref_primary_10_1002_cyto_a_23918 crossref_primary_10_1016_0038_1101_95_00117_C crossref_primary_10_1038_s41416_018_0210_y crossref_primary_10_1016_0010_4655_84_90147_4 crossref_primary_10_1007_s11760_012_0341_1 crossref_primary_10_1109_TIA_2013_2272051 crossref_primary_10_1016_0921_8181_94_90017_5 crossref_primary_10_1016_S0890_6955_00_00107_3 crossref_primary_10_1109_36_263771 crossref_primary_10_1016_j_ces_2009_12_028 crossref_primary_10_1117_1_JRS_8_083676 crossref_primary_10_1007_s10589_019_00064_2 crossref_primary_10_1007_s10822_006_9098_3 crossref_primary_10_1364_AO_37_000130 crossref_primary_10_1016_j_jaerosci_2010_12_004 crossref_primary_10_1016_S0890_6955_97_00136_3 crossref_primary_10_1109_21_141309 crossref_primary_10_1109_20_106394 crossref_primary_10_1109_JSEN_2024_3417289 crossref_primary_10_1117_1_OE_55_12_123103 crossref_primary_10_1364_OE_15_018275 crossref_primary_10_1016_j_tca_2016_02_007 crossref_primary_10_1109_TITS_2023_3299557 crossref_primary_10_1529_biophysj_106_100891 crossref_primary_10_1016_0020_7403_85_90081_5 crossref_primary_10_2136_sssaj2010_0307 crossref_primary_10_1007_BF02591997 crossref_primary_10_1021_acs_analchem_5b04820 crossref_primary_10_1016_j_applthermaleng_2010_06_006 crossref_primary_10_1109_72_548172 crossref_primary_10_1016_j_xphs_2016_04_002 crossref_primary_10_1017_S1539299600008613 crossref_primary_10_1007_s40261_013_0148_z crossref_primary_10_1190_geo2018_0254_1 crossref_primary_10_1007_s11750_019_00497_2 crossref_primary_10_3390_rs13173480 crossref_primary_10_1080_01431161_2024_2313993 crossref_primary_10_1109_JSEN_2020_2978129 crossref_primary_10_1007_s40096_020_00339_4 crossref_primary_10_1016_0021_8634_92_80037_S crossref_primary_10_1023_B_JOTA_0000005041_99777_af crossref_primary_10_1029_WR020i001p00089 crossref_primary_10_3389_fams_2017_00006 crossref_primary_10_3788_LOP232616 crossref_primary_10_1007_s11004_018_9742_1 crossref_primary_10_1016_0167_4838_88_90020_9 crossref_primary_10_3758_BF03205922 crossref_primary_10_1080_01431161_2020_1809743 crossref_primary_10_1177_004051759106101101 crossref_primary_10_1155_2014_794630 crossref_primary_10_1007_s11075_016_0101_3 crossref_primary_10_1021_jp803260n crossref_primary_10_1007_s40435_020_00686_z crossref_primary_10_1109_TSG_2016_2595759 crossref_primary_10_3390_en15155587 crossref_primary_10_1021_la800770y crossref_primary_10_3103_S009545271005004X crossref_primary_10_1002_jsfa_2740350702 crossref_primary_10_1016_0168_9002_88_90726_7 crossref_primary_10_1144_petgeo2017_052 crossref_primary_10_1080_17480272_2021_1967447 crossref_primary_10_1364_OE_20_000299 crossref_primary_10_1007_BF03031828 crossref_primary_10_1177_0954406218771100 crossref_primary_10_1115_1_4002922 crossref_primary_10_1117_1_JMI_9_4_045003 crossref_primary_10_1016_S0021_9258_18_81759_8 crossref_primary_10_1021_jp800525w crossref_primary_10_1002_pssa_2211350105 crossref_primary_10_1137_100798181 crossref_primary_10_1111_j_1365_2435_2011_01866_x crossref_primary_10_1061__ASCE_WR_1943_5452_0001273 crossref_primary_10_1109_TPWRS_2015_2409116 crossref_primary_10_1080_08839514_2017_1378162 crossref_primary_10_1109_LSP_2013_2284971 crossref_primary_10_1088_0022_3735_20_3_009 crossref_primary_10_1103_PhysRevB_31_3846 crossref_primary_10_1109_TAES_2023_3269736 crossref_primary_10_1080_03610928708829416 crossref_primary_10_3390_app12052622 crossref_primary_10_1016_0020_7101_84_90040_0 crossref_primary_10_1016_0022_2364_86_90107_1 crossref_primary_10_1016_j_corsci_2013_05_018 crossref_primary_10_1137_0910033 crossref_primary_10_1016_j_trc_2013_05_011 crossref_primary_10_1109_ACCESS_2018_2881990 crossref_primary_10_1364_OE_505822 crossref_primary_10_1364_OE_27_028832 crossref_primary_10_1016_0020_7403_90_90150_H crossref_primary_10_1080_00387019508009457 crossref_primary_10_1061__ASCE_0733_9429_1994_120_7_787 crossref_primary_10_1016_0375_9474_87_90436_2 crossref_primary_10_1186_1471_230X_9_64 crossref_primary_10_1103_PhysRevE_98_052408 crossref_primary_10_1016_S0013_4694_97_00142_9 crossref_primary_10_1109_TPWRS_1987_4335070 crossref_primary_10_1137_0906071 crossref_primary_10_1016_j_corsci_2009_08_030 crossref_primary_10_1080_01431161_2024_2440670 crossref_primary_10_1117_1_3364071 crossref_primary_10_1016_0040_1951_91_90132_C crossref_primary_10_1103_PhysRevA_101_012321 crossref_primary_10_1016_0771_050X_79_90011_1 crossref_primary_10_1364_OE_21_026942 crossref_primary_10_2463_mrms_rev_2021_0005 crossref_primary_10_1016_j_chemphys_2016_05_007 crossref_primary_10_1080_02331934_2011_652810 crossref_primary_10_1049_iet_ipr_2012_0614 crossref_primary_10_1016_0009_3084_93_90025_X crossref_primary_10_1016_S0090_9556_24_15056_8 crossref_primary_10_1080_01431161_2020_1851795 crossref_primary_10_1002_cite_201500165 crossref_primary_10_1007_s10589_006_6444_2 crossref_primary_10_1029_91JE01773 crossref_primary_10_1080_00288306_1989_10421394 crossref_primary_10_1103_PhysRevE_83_036701 crossref_primary_10_1140_epjp_s13360_024_05746_3 crossref_primary_10_1155_2014_193758 crossref_primary_10_1016_0014_3057_83_90037_X crossref_primary_10_1038_s41598_024_77675_1 crossref_primary_10_1080_01431168308948560 crossref_primary_10_1109_TE_1986_5570562 crossref_primary_10_1134_S1063783417040023 crossref_primary_10_1002_sim_4780122106 crossref_primary_10_3905_jod_2011_2011_1_010 crossref_primary_10_1016_0260_8774_92_90001_M crossref_primary_10_1016_j_conengprac_2011_10_010 crossref_primary_10_1109_52_84215 crossref_primary_10_1002_maco_201911375 crossref_primary_10_1007_BF01385741 crossref_primary_10_1016_j_tecto_2014_01_016 crossref_primary_10_1016_S1003_6326_24_66600_8 crossref_primary_10_1080_004982599238074 crossref_primary_10_1115_1_2838039 crossref_primary_10_1002_jat_1511 crossref_primary_10_1016_0167_8191_88_90138_X crossref_primary_10_1016_j_cplett_2007_02_046 crossref_primary_10_1016_j_corsci_2014_07_060 crossref_primary_10_1007_BF00945453 crossref_primary_10_1007_s11517_023_02815_0 crossref_primary_10_1002_bimj_4710260505 crossref_primary_10_1016_j_corsci_2015_02_002 crossref_primary_10_1016_0040_6031_91_85239_E crossref_primary_10_1016_j_jvcir_2013_04_008 crossref_primary_10_1002_er_4022 crossref_primary_10_14801_JAITC_2020_10_1_25 crossref_primary_10_1109_TBME_1987_325929 crossref_primary_10_1111_j_1475_097X_1984_tb00229_x crossref_primary_10_1016_0021_9290_88_90143_1 crossref_primary_10_1016_j_econmod_2008_04_001 crossref_primary_10_1080_00387019808001659 crossref_primary_10_1016_j_chemphys_2007_06_047 crossref_primary_10_1016_j_corsci_2019_01_042 crossref_primary_10_1016_j_ijheatmasstransfer_2016_06_044 crossref_primary_10_1002_bit_260341012 crossref_primary_10_1016_j_mechatronics_2013_09_007 crossref_primary_10_1016_S0040_6031_99_00510_9 crossref_primary_10_1080_00268978400100441 crossref_primary_10_1088_0022_3727_43_2_025209 crossref_primary_10_1111_j_1475_1305_2009_00637_x crossref_primary_10_1016_j_jtbi_2015_12_023 crossref_primary_10_1109_14_68229 crossref_primary_10_1002_adem_201400434 crossref_primary_10_1016_j_exger_2007_08_002 crossref_primary_10_1103_PhysRevApplied_17_034062 crossref_primary_10_1002_gamm_200790023 crossref_primary_10_1007_s11694_022_01522_y crossref_primary_10_18698_1812_3368_2021_3_64_76 crossref_primary_10_1137_0908042 crossref_primary_10_5194_npg_23_59_2016 crossref_primary_10_3390_w7010051 crossref_primary_10_1007_BF01390425 crossref_primary_10_1061__ASCE_0733_950X_1997_123_2_68 crossref_primary_10_1080_10934529_2013_823333 crossref_primary_10_1109_TIM_2014_2303553 |
| Cites_doi | 10.1093/comjnl/9.1.67 10.1007/BF00930579 10.1080/00401706.1968.10490535 10.1147/rd.165.0504 10.1093/comjnl/3.3.175 10.1093/comjnl/8.1.33 10.1093/comjnl/6.2.163 10.1093/comjnl/10.4.392 10.1007/BF01585529 10.1093/comjnl/5.2.147 10.1007/BF01681328 10.1016/B978-0-12-148950-2.50010-9 10.1287/mnsc.13.5.344 10.1007/BF00935703 10.1145/321186.321200 10.1007/BFb0080120 10.1137/0707011 10.1007/BF00932656 |
| ContentType | Journal Article |
| Copyright | Copyright 1978 Society for Industrial and Applied Mathematics [Copyright] © 1978 Society for Industrial and Applied Mathematics |
| Copyright_xml | – notice: Copyright 1978 Society for Industrial and Applied Mathematics – notice: [Copyright] © 1978 Society for Industrial and Applied Mathematics |
| DBID | AAYXX CITATION 3V. 7WY 7WZ 7X2 7XB 87Z 88A 88F 88I 88K 8AL 8FE 8FG 8FH 8FK 8FL 8G5 ABJCF ABUWG AFKRA ARAPS ATCPS AZQEC BBNVY BENPR BEZIV BGLVJ BHPHI CCPQU D1I DWQXO FRNLG F~G GNUQQ GUQSH HCIFZ JQ2 K60 K6~ K7- KB. L.- L6V LK8 M0C M0K M0N M1Q M2O M2P M2T M7P M7S MBDVC P5Z P62 PATMY PDBOC PHGZM PHGZT PKEHL PQBIZ PQBZA PQEST PQGLB PQQKQ PQUKI PRINS PTHSS PYCSY Q9U |
| DOI | 10.1137/0715063 |
| DatabaseName | CrossRef ProQuest Central (Corporate) ABI/INFORM Collection ABI/INFORM Global (PDF only) Agricultural Science Collection ProQuest Central (purchase pre-March 2016) ABI/INFORM Collection Biology Database (Alumni Edition) Military Database (Alumni Edition) Science Database (Alumni Edition) Telecommunications (Alumni Edition) Computing Database (Alumni Edition) ProQuest SciTech Collection ProQuest Technology Collection ProQuest Natural Science Journals ProQuest Central (Alumni) (purchase pre-March 2016) ABI/INFORM Collection (Alumni) Research Library Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection Agricultural & Environmental Science Collection ProQuest Central Essentials - QC Biological Science Collection ProQuest Central Business Premium Collection Technology Collection Natural Science Collection ProQuest One Community College ProQuest Materials Science Collection ProQuest Central Business Premium Collection (Alumni) ABI/INFORM Global (Corporate) ProQuest Central Student ProQuest Research Library SciTech Premium Collection ProQuest Computer Science Collection ProQuest Business Collection (Alumni Edition) ProQuest Business Collection Computer Science Database Materials Science Database ABI/INFORM Professional Advanced ProQuest Engineering Collection Biological Sciences ABI Inform Agricultural Science Database Computing Database Military Database Research Library Science Database Telecommunications Database Biological Science Database Engineering Database Research Library (Corporate) Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection Environmental Science Database Materials Science Collection Proquest Central Premium ProQuest One Academic ProQuest One Academic Middle East (New) ProQuest One Business ProQuest One Business (Alumni) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection Environmental Science Collection ProQuest Central Basic |
| DatabaseTitle | CrossRef Agricultural Science Database ProQuest Business Collection (Alumni Edition) Research Library Prep Computer Science Database ProQuest Central Student ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection SciTech Premium Collection ProQuest Military Collection ProQuest Central China ABI/INFORM Complete ProQuest Telecommunications ProQuest One Applied & Life Sciences Natural Science Collection Biological Science Collection ProQuest Central (New) Engineering Collection Advanced Technologies & Aerospace Collection Business Premium Collection ABI/INFORM Global Engineering Database ProQuest Science Journals (Alumni Edition) ProQuest Biological Science Collection ProQuest One Academic Eastern Edition Agricultural Science Collection ProQuest Technology Collection ProQuest Telecommunications (Alumni Edition) Biological Science Database ProQuest Business Collection Environmental Science Collection ProQuest One Academic UKI Edition Environmental Science Database ProQuest One Academic ProQuest One Academic (New) ABI/INFORM Global (Corporate) ProQuest One Business Technology Collection ProQuest One Academic Middle East (New) Materials Science Collection ProQuest Central (Alumni Edition) ProQuest One Community College Research Library (Alumni Edition) ProQuest Natural Science Collection ProQuest Biology Journals (Alumni Edition) ProQuest Central ABI/INFORM Professional Advanced ProQuest Engineering Collection ProQuest Central Korea Agricultural & Environmental Science Collection Materials Science Database ProQuest Research Library ABI/INFORM Complete (Alumni Edition) ProQuest Materials Science Collection ProQuest Computing ABI/INFORM Global (Alumni Edition) ProQuest Central Basic ProQuest Science Journals ProQuest Computing (Alumni Edition) ProQuest Military Collection (Alumni Edition) ProQuest SciTech Collection Advanced Technologies & Aerospace Database Materials Science & Engineering Collection ProQuest One Business (Alumni) ProQuest Central (Alumni) Business Premium Collection (Alumni) |
| DatabaseTitleList | Agricultural Science Database |
| Database_xml | – sequence: 1 dbid: 8FG name: ProQuest Technology Collection url: https://search.proquest.com/technologycollection1 sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Mathematics |
| EISSN | 1095-7170 |
| EndPage | 992 |
| ExternalDocumentID | 2595769801 10_1137_0715063 2156716 |
| GroupedDBID | -DZ -~X 123 2AX 3R3 4.4 7WY 7X2 7XC 88I 8CJ 8FE 8FG 8FH 8FL 8G5 AALVN AAWIL ABAWQ ABBHK ABFAN ABJCF ABPFR ABPQH ABUWG ABXSQ ABYWD ACBEA ACGFO ACGOD ACHJO ACIWK ACMTB ACNCT ACPRK ACTMH ACUBG ADBBV ADODI ADULT AENEX AEUPB AFKRA AFRAH AFVYC AFXHP AGLNM AIHAF ALMA_UNASSIGNED_HOLDINGS ALRMG ARAPS ATCPS AZQEC BBNVY BENPR BEZIV BGLVJ BHPHI BPHCQ CCPQU CS3 CZ9 D1I D1J D1K DQDLB DSRWC DU5 DWQXO EBS ECEWR EJD ESX FEDTE FRNLG FVMVE GNUQQ GUQSH HCIFZ HGD HQ6 HVGLF IPSME JAAYA JAS JBMMH JBZCM JENOY JHFFW JKQEH JLEZI JLXEF JMS JPL JST K6- K60 K6V K6~ K7- KB. KC. L6V LK5 LK8 M0C M0K M1Q M2O M2P M7P M7R M7S MVM N9A NHB P1Q P2P P62 PATMY PDBOC PHGZM PHGZT PQBIZ PQBZA PQQKQ PROAC PTHSS PYCSY RJG RNS RSI SA0 T9H TN5 WH7 YNT YXE .4S .DC 3EH 8WZ A6W AASXH AAYJJ AAYXX ABDBF ABKAD ABMZU ACUHS ANXRF ARCSS CITATION DQ2 EAP EDO EMK EST H13 H~9 I-F P0- PQGLB PUEGO TAE TUS WHG ZCG 3V. 7XB 88A 88K 8AL 8FK JQ2 L.- M0N M2T MBDVC PKEHL PQEST PQUKI PRINS Q9U |
| ID | FETCH-LOGICAL-c1848-a09869b2146518be3d5fecd0b73edfbaf248cdac442d1378aec0b301a133d5e43 |
| IEDL.DBID | BENPR |
| ISSN | 0036-1429 |
| IngestDate | Mon Aug 25 14:14:37 EDT 2025 Thu Apr 24 22:59:45 EDT 2025 Wed Oct 01 03:44:30 EDT 2025 Thu Jun 19 15:12:33 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 5 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c1848-a09869b2146518be3d5fecd0b73edfbaf248cdac442d1378aec0b301a133d5e43 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 content type line 14 |
| PQID | 923620898 |
| PQPubID | 666303 |
| PageCount | 16 |
| ParticipantIDs | proquest_journals_923620898 crossref_citationtrail_10_1137_0715063 crossref_primary_10_1137_0715063 jstor_primary_2156716 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 1900 |
| PublicationDate | 19781001 1978-10-00 |
| PublicationDateYYYYMMDD | 1978-10-01 |
| PublicationDate_xml | – month: 10 year: 1978 text: 19781001 day: 1 |
| PublicationDecade | 1970 |
| PublicationPlace | Philadelphia |
| PublicationPlace_xml | – name: Philadelphia |
| PublicationTitle | SIAM journal on numerical analysis |
| PublicationYear | 1978 |
| Publisher | Society for Industrial and Applied Mathematics |
| Publisher_xml | – name: Society for Industrial and Applied Mathematics |
| References | R3 Lawson Charles L. (R24) 1974 R4 R5 R8 R9 Osborne M. R. (R27) 1972 R30 R10 R20 R11 R22 R14 R13 R16 R15 R29 R28 Kowalik J. (R23) 1968 R19 Brent Richard P. (R6) 1973 R1 |
| References_xml | – ident: R4 doi: 10.1093/comjnl/9.1.67 – ident: R8 doi: 10.1007/BF00930579 – ident: R22 doi: 10.1080/00401706.1968.10490535 – ident: R5 doi: 10.1147/rd.165.0504 – ident: R29 doi: 10.1093/comjnl/3.3.175 – volume-title: Algorithms for minimization without derivatives year: 1973 ident: R6 – ident: R13 doi: 10.1093/comjnl/8.1.33 – ident: R15 doi: 10.1093/comjnl/6.2.163 – ident: R14 doi: 10.1093/comjnl/10.4.392 – ident: R19 doi: 10.1007/BF01585529 – start-page: 171 volume-title: Numerical methods for non-linear optimization (Conf., Univ. Dundee, Dundee, 1971) year: 1972 ident: R27 – ident: R28 doi: 10.1093/comjnl/5.2.147 – ident: R9 doi: 10.1007/BF01681328 – ident: R11 doi: 10.1016/B978-0-12-148950-2.50010-9 – ident: R30 doi: 10.1287/mnsc.13.5.344 – ident: R10 doi: 10.1007/BF00935703 – ident: R16 doi: 10.1145/321186.321200 – ident: R20 doi: 10.1007/BFb0080120 – volume-title: Solving least squares problems year: 1974 ident: R24 – ident: R1 doi: 10.1137/0707011 – volume-title: Methods for unconstrained optimization problems year: 1968 ident: R23 – ident: R3 doi: 10.1007/BF00932656 |
| SSID | ssj0003813 |
| Score | 1.242048 |
| Snippet | This paper describes a modification to the Gauss-Newton method for the solution of nonlinear least-squares problems. The new method seeks to avoid the... |
| SourceID | proquest crossref jstor |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 977 |
| SubjectTerms | Algorithms Approximation Curvature Factorization Hessian matrices Laboratories Least squares Local minimum Mathematical functions Matrices Scalars |
| Title | Algorithms for the Solution of the Nonlinear Least-Squares Problem |
| URI | https://www.jstor.org/stable/2156716 https://www.proquest.com/docview/923620898 |
| Volume | 15 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: http://www.proquest.com/pqcentral?accountid=15518 eissn: 1095-7170 dateEnd: 20140531 omitProxy: true ssIdentifier: ssj0003813 issn: 0036-1429 databaseCode: BENPR dateStart: 19660101 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Technology Collection customDbUrl: eissn: 1095-7170 dateEnd: 20140531 omitProxy: true ssIdentifier: ssj0003813 issn: 0036-1429 databaseCode: 8FG dateStart: 19640101 isFulltext: true titleUrlDefault: https://search.proquest.com/technologycollection1 providerName: ProQuest |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1JS8NAFH50uejBpVas1TIH8RacbO3kINJKaxFbilroLcwWPdTu_f--SSYBKXgMMwTmZd7yTd58H8CdpyhDrxGOx4V2AomYNaJaOpxKzTTmoFCl3Rbj9nAavM7CWQlG-V0Y01aZx8Q0UKulNGfkD1iItD3KIva0WjtGNMr8XM0VNLhVVlCPKcNYGaqeIcaqQLXXH0_ei9CM6alg4XUxEme3aF3XkPx0DNee_yc9ZR2KB1E6TT2DMzixNSPpZh_5HEp6UYNTWz8S653bGhyPCg7W7QX0uvMvXMHu-2dLsDIlOETyQzCyTNLncUaUwTfkzWj4OB_rvbmPRCaZzEwdpoP-5_PQsYoJjkSkxtDCEWtHwoh1oxmE9lWYaKmo6PhaJYInXsCk4jIIPIWLZlxLKtDFOSJVFerAv4TKYrnQV0ACqnxXYfWHL0QQhUBZeDSRbhIhBOTUb8B9bqhYWjpxo2oxj1NY4Xdia9EGkGLiKmPQOJxSTy1djGMd0kYg14BmbvnYutY2LjbC9b-jTThyU4Rs-u5uoLLb7PUt1g870YIyG7y07N74BSJ5w-A |
| linkProvider | ProQuest |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3JTsMwEB0BPQAHdkQpiw_ALcKJ3TY5IERZVKBUiEXiFrwFDqULaYX4OP6NceJEQkjcOEZ2rGgynpmXjN8D2As0DXHXSC8Q0nhcIWaNqFGeoMqEBnNQXWfdFt1G-5FfPdWfpuCrOAtj2yqLmJgFaj1Q9hv5IRYijYCGUXg8HHlWNMr-XC0UNIRTVtBHGcOYO9dxbT4_EMGlR5dn-Lr3g-Di_OG07TmRAU8huAnxoaKwEUmrb413SsN0PTFKU9lkRidSJAEPlRaK80D7rBkKo6jEXSEQ3Om64QzXnYYKZzxC7FdpnXdv78pUgOmwZP31MfLnp3Z935IKNS23H_uRDvOOyF9ZIUt1F0uw4GpUcpI71TJMmf4KLLp6lbhokK7A_E3J-ZquQuuk94IWG7--pQQrYYJDpPjoRgZJdt3NiTnEO-lYzSDvfjSx55_IbS5rswaP_2K8dZjpD_pmAwinmvkaq01cEEEbAnMZ0ET5SYSQU1BWhYPCULFy9OVWRaMXZzCGNWNn0SqQcuIwZ-z4PWUts3Q5jnVPA4FjFWqF5WO3ldO4dLzNP0d3Ybb9cNOJO5fd6xrM-Rk6tz1_WzAzfp-YbaxdxnLHeQiB5_92ym-EtACb |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Algorithms+for+the+Solution+of+the+Nonlinear+Least-Squares+Problem&rft.jtitle=SIAM+journal+on+numerical+analysis&rft.au=Gill%2C+Philip+E&rft.au=Murray%2C+Walter&rft.date=1978-10-01&rft.pub=Society+for+Industrial+and+Applied+Mathematics&rft.issn=0036-1429&rft.eissn=1095-7170&rft.volume=15&rft.issue=5&rft.spage=977&rft_id=info:doi/10.1137%2F0715063&rft.externalDocID=2595769801 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0036-1429&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0036-1429&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0036-1429&client=summon |