/LMAR=0/XLINE=10/FONT#0=SAIL25
␈↓ α∧␈↓January␈↓ ε≡1979 Reports␈↓ s1

␈↓"β␈↓ α∧␈↓␈↓ ∧IMOST RECENT CS REPORTS - JANUARY 1979

␈↓"β␈↓ α∧␈↓    Listed␈α∪below␈α∪are␈α∪abstracts␈α∪of␈α∪the␈α∪most␈α∪recent␈α∪reports␈α∪published␈α∪by␈α∪the
␈↓ α∧␈↓Computer Science Department of Stanford University.

␈↓"β␈↓ α∧␈↓    TO␈α∩REQUEST␈α⊃REPORTS:␈α∩ Check␈α⊃the␈α∩appropriate␈α⊃places␈α∩on␈α⊃the␈α∩enclosed␈α⊃order
␈↓ α∧␈↓form,␈α⊗and␈α⊗return␈α⊗the␈α⊗entire␈α⊗order␈α⊗form␈α⊗page␈α⊗(including␈α⊗mailing␈α↔label)␈α⊗by
␈↓ α∧␈↓January␈α_19,␈α_1979.␈α_ In␈α_many␈α_cases␈α_we␈α_can␈α_print␈α_only␈α_a␈α_limited␈α_number␈α↔of
␈↓ α∧␈↓copies,␈α⊃and␈α∩requests␈α⊃will␈α⊃be␈α∩filled␈α⊃on␈α∩a␈α⊃first␈α⊃come,␈α∩first␈α⊃serve␈α∩basis.␈α⊃ If
␈↓ α∧␈↓the␈α∀code␈α∀(FREE)␈α∀is␈α∀printed␈α∀on␈α∀your␈α∀mailing␈α∀label,␈α∀you␈α∀will␈α∀not␈α∀be␈α∀charged
␈↓ α∧␈↓for␈α#hardcopy.␈α" This␈α#exemption␈α"from␈α#payment␈α"is␈α#limited␈α#primarily␈α"to
␈↓ α∧␈↓libraries.␈α↔ (The␈α↔costs␈α↔shown␈α_include␈α↔all␈α↔applicable␈α↔sales␈α_taxes.␈α↔ PLEASE
␈↓ α∧␈↓SEND NO MONEY NOW, WAIT UNTIL YOU GET AN INVOICE.)

␈↓"β␈↓ α∧␈↓    ALTERNATIVELY:␈α∃ Copies␈α∃of␈α∃most␈α∃Stanford␈α∃CS␈α∃Reports␈α∃may␈α∃be␈α∃obtained␈α∀by
␈↓ α∧␈↓writing␈α∃(about␈α∀2␈α∃months␈α∀after␈α∃MOST␈α∀RECENT␈α∃CS␈α∀REPORTS␈α∃listing)␈α∃to␈α∀NATIONAL
␈↓ α∧␈↓TECHNICAL␈α∀INFORMATION␈α∀SERVICE,␈α∀5285␈α∪Port␈α∀Royal␈α∀Road,␈α∀Springfield,␈α∪Virginia
␈↓ α∧␈↓22161.␈α∩ Stanford␈α⊃Ph.D.␈α∩theses␈α⊃are␈α∩available␈α⊃from␈α∩UNIVERSITY␈α∩MICROFILMS,␈α⊃300
␈↓ α∧␈↓North Zeeb Road, Ann Arbor, Michigan 48106.
␈↓"β␈↓ α∧␈↓--------------------------------------------------------------------------
␈↓"β␈↓ α∧␈↓--------------------------------------------------------------------------
␈↓"β␈↓ α∧␈↓STAN-CS-79-691  THE CONSTRUCTION OF INITIAL DATA FOR HYPERBOLIC SYSTEMS
␈↓"β␈↓ α∧␈↓                FROM NONSTANDARD DATA
␈↓"β␈↓ α∧␈↓Author:  Kenneth P. Bube␈↓ 
|(Thesis)

␈↓"β␈↓ α∧␈↓    Abstract:␈α≥ We␈α≥study␈α≥the␈α≥first␈α≥order␈α≥systems␈α≥of␈α≥hyperbolic␈α≤partial
␈↓ α∧␈↓differential␈α≡equations␈α∨with␈α≡periodic␈α≡boundary␈α∨conditions␈α≡in␈α∨the␈α≡space
␈↓ α∧␈↓variables␈α↔for␈α⊗which␈α↔complete␈α↔initial␈α⊗data␈α↔are␈α⊗not␈α↔available.␈α↔ We␈α⊗suppose
␈↓ α∧␈↓that␈α↔we␈α↔can␈α↔measure␈α↔u␈↓#
I␈↓#␈α↔,␈α↔the␈α↔first␈α↔j␈α↔components␈α↔of␈α↔a␈α↔solution␈α↔u␈α↔of␈α↔the
␈↓ α∧␈↓system,␈α_perhaps␈α↔with␈α_its␈α_time␈α↔derivatives,␈α_but␈α_cannot␈α↔measure␈α_u␈↓#
II␈↓#␈α_,␈α↔the
␈↓ α∧␈↓rest␈α∪of␈α∪the␈α∩components␈α∪of␈α∪u␈α∩,␈α∪completely␈α∪and␈α∩accurately␈α∪at␈α∪any␈α∪time␈α∩level.
␈↓ α∧␈↓Such␈α∪problems␈α∪arise␈α∪in␈α∀geophysical␈α∪application␈α∪where␈α∪satelites␈α∪are␈α∀used␈α∪to
␈↓ α∧␈↓collect␈α∪data.␈α∪ We␈α∪consider␈α∪two␈α∪questions.␈α∪ How␈α∪much␈α∪information␈α∪do␈α∪we␈α∪need
␈↓ α∧␈↓to␈α⊃determine␈α∩the␈α⊃solution␈α∩u␈α⊃uniquely␈α⊃in␈α∩a␈α⊃way␈α∩which␈α⊃depends␈α∩continuously␈α⊃on
␈↓ α∧␈↓the␈α≠data?␈α≠ How␈α~do␈α≠we␈α≠use␈α≠these␈α~data␈α≠compuationally␈α≠to␈α≠obtain␈α~complete
␈↓ α∧␈↓initial data at some time level?

␈↓"β␈↓ α∧␈↓    We␈α~investigate␈α~several␈α~approaches␈α~to␈α~answering␈α~these␈α≠questions.␈α~ We
␈↓ α∧␈↓show␈α⊗that␈α⊗under␈α⊗certain␈α⊗hypotheses␈α⊗u␈↓#
II␈↓#␈α⊗at␈α⊗the␈α⊗initial␈α⊗time␈α↔is␈α⊗determined
␈↓ α∧␈↓uniquely␈α~by␈α~and␈α~depends␈α~continuously␈α~on␈α~the␈α~data␈α~obtained␈α~by␈α~measuring
␈↓ α∧␈↓either␈α⊃u␈↓#
I␈↓#␈α∩over␈α⊃a␈α⊃whole␈α∩time␈α⊃interval␈α⊃or␈α∩u␈↓#
I␈↓#␈α⊃and␈α⊃its␈α∩first␈α⊃time␈α∩derivative␈α⊃at
␈↓ α∧␈↓the␈α∀initial␈α∀time,␈α∀together␈α∀ith␈α∀either␈α∀u␈↓#
II␈↓#␈α∀on␈α∀a␈α∀hyperplane␈α∀in␈α∀space␈α∀of␈α∀one
␈↓ α∧␈↓lower␈α⊗dimension␈α⊗or␈α∃a␈α⊗finite␈α⊗number␈α∃of␈α⊗Fourier␈α⊗coefficients␈α∃of␈α⊗u␈↓#
II␈↓#␈α⊗at␈α∃the
␈↓ α∧␈↓initial␈α⊗time.␈α⊗ Our␈α⊗results␈α⊗demonstrate␈α⊗that␈α⊗it␈α⊗is␈α⊗possible␈α⊗to␈α↔reduce␈α⊗the
␈↓ α∧␈↓data requirements of u␈↓#
II␈↓# if sufficient information about u␈↓#
I␈↓# is available.
␈↓ α∧␈↓January␈↓ ε≡1979 Reports␈↓ s2

␈↓"β␈↓ α∧␈↓    One␈α↔appliction␈α↔we␈α↔examine␈α↔is␈α↔the␈α↔effect␈α↔of␈α↔the␈α↔Coriolis␈α↔term␈α_in␈α↔the
␈↓ α∧␈↓linearized␈α→shallow␈α→water␈α→equations␈α→on␈α→the␈α→possibility␈α→of␈α~recovering␈α→the
␈↓ α∧␈↓wind fields from the geopotential height.

␈↓"β␈↓ α∧␈↓    We␈α_present␈α_algorithms␈α_and␈α_computational␈α_results␈α_for␈α_these␈α_approaches
␈↓ α∧␈↓for␈α~a␈α~model␈α~two-by-two␈α~system,␈α~and␈α~examine␈α~the␈α~method␈α~for␈α~intermittent
␈↓ α∧␈↓updating␈α∃currently␈α∃being␈α∃used␈α∃in␈α∃numerical␈α∃weather␈α∃prediction␈α∃as␈α∃a␈α∀method
␈↓ α∧␈↓for␈α∨the␈α assimilation␈α∨of␈α∨data.␈α  Our␈α∨results␈α∨suggest␈α that␈α∨the␈α use␈α∨of
␈↓ α∧␈↓different frequencies of updating is important to avoid slow convergence.
␈↓"β␈↓ α∧␈↓No. of pages:  119
␈↓"β␈↓ α∧␈↓Available in microfiche only.
␈↓"β␈↓ α∧␈↓--------------------------------------------------------------------------
␈↓"β␈↓ α∧␈↓HPP-77-39  MODELS OF LEARNING SYSTEMS
␈↓"β␈↓ α∧␈↓Authors:  Bruce G. Buchanan, Tom M. Mitchell, Reid G. Smith
␈↓"β␈↓ α∧␈↓          & C. Richard Johnson Jr.

␈↓"β␈↓ α∧␈↓    Abstract:␈α4 The␈α4terms␈α4adaptation,␈α4learning,␈α4concept-formation,
␈↓ α∧␈↓induction,␈α→self-organization,␈α→and␈α→self-repair␈α→have␈α→all␈α→been␈α→used␈α~in␈α→the
␈↓ α∧␈↓context␈α∪of␈α∪learning␈α∪system␈α∀(LS)␈α∪research.␈α∪ In␈α∪this␈α∪article,␈α∀three␈α∪distinct
␈↓ α∧␈↓approaches␈α≠to␈α≠machine␈α≠learning␈α≠and␈α≠adaptation␈α≠are␈α≠considered:␈α≠ (i)␈α≠the
␈↓ α∧␈↓adaptive␈α∩control␈α⊃approach,␈α∩(ii)␈α⊃the␈α∩pattern␈α⊃recognition␈α∩approach,␈α∩and␈α⊃(iii)
␈↓ α∧␈↓the artificial intelligence approach.

␈↓"β␈↓ α∧␈↓    Progress␈α∪in␈α∪each␈α∩of␈α∪these␈α∪areas␈α∩is␈α∪summarized␈α∪in␈α∩the␈α∪first␈α∪part␈α∪of␈α∩the
␈↓ α∧␈↓article.␈α∨ In␈α the␈α∨next␈α∨part␈α a␈α∨general␈α∨model␈α for␈α∨learning␈α systems␈α∨is
␈↓ α∧␈↓presented␈α%that␈α%allows␈α%characterization␈α%and␈α%comparison␈α&of␈α%individual
␈↓ α∧␈↓algorithms␈α!and␈α!programs␈α!in␈α!all␈α these␈α!areas.␈α! The␈α!model␈α!details␈α the
␈↓ α∧␈↓functional␈α!components␈α!felt␈α to␈α!be␈α!essential␈α for␈α!any␈α!learning␈α system,
␈↓ α∧␈↓independent␈α∃of␈α∃the␈α∃techniques␈α∃used␈α∃for␈α∃its␈α∃construction,␈α∃and␈α∃the␈α∀specific
␈↓ α∧␈↓environment␈α↔in␈α↔which␈α↔it␈α_operates.␈α↔ Specific␈α↔examples␈α↔of␈α_learning␈α↔systems
␈↓ α∧␈↓are described in terms of the model.
␈↓"β␈↓ α∧␈↓No. of pages:  38
␈↓"β␈↓ α∧␈↓Cost:  $ 2.80
␈↓"β␈↓ α∧␈↓--------------------------------------------------------------------------
␈↓"β␈↓ α∧␈↓STAN-CS-79-693  A CLASS OF SOLUTIONS TO THE GOSSIP PROBLEM
␈↓"β␈↓ α∧␈↓Author:  Douglas B. West

␈↓"β␈↓ α∧␈↓    Abstract:␈α↔ We␈α↔characterize␈α↔and␈α_count␈α↔optimal␈α↔solutions␈α↔to␈α_the␈α↔gossip
␈↓ α∧␈↓problem␈α⊗in␈α⊗which␈α∃no␈α⊗one␈α⊗hears␈α∃his␈α⊗own␈α⊗information.␈α∃ That␈α⊗is,␈α⊗we␈α∃consider
␈↓ α∧␈↓graphs␈α∪with␈α∪n␈α∩vertices␈α∪where␈α∪the␈α∩edges␈α∪have␈α∪a␈α∩linear␈α∪ordering␈α∪such␈α∪that␈α∩an
␈↓ α∧␈↓increasing␈α↔path␈α↔exists␈α↔from␈α↔each␈α↔vertex␈α↔to␈α↔every␈α↔other,␈α↔but␈α↔there␈α_is␈α↔no
␈↓ α∧␈↓increasing␈α∀path␈α∀from␈α∃any␈α∀vertex␈α∀to␈α∀itself.␈α∃ Such␈α∀graphs␈α∀exist␈α∀only␈α∃when␈α∀n
␈↓ α∧␈↓is␈α~even,␈α~in␈α~which␈α~case␈α~the␈α~fewest␈α→number␈α~of␈α~edges␈α~is␈α~2n-4,␈α~as␈α~in␈α→the
␈↓ α∧␈↓original␈α↔gossip␈α↔problem.␈α↔ We␈α_characterize␈α↔optimal␈α↔solutions␈α↔of␈α_this␈α↔sort
␈↓ α∧␈↓(NOHO-graphs)␈α∪using␈α∪a␈α∪correspondence␈α∀with␈α∪a␈α∪set␈α∪of␈α∪permutations␈α∀and␈α∪binary
␈↓ α∧␈↓sequences.␈α→ This␈α→correspondence␈α→enables␈α→us␈α→to␈α→count␈α→these␈α~solutions␈α→and
␈↓ α∧␈↓several␈α↔subclasses␈α⊗of␈α↔solutions.␈α↔ The␈α⊗numbers␈α↔of␈α⊗solutions␈α↔in␈α↔each␈α⊗class
␈↓ α∧␈↓January␈↓ ε≡1979 Reports␈↓ s3

␈↓"β␈↓ α∧␈↓are␈α⊃simple␈α∩powers␈α⊃of␈α⊃2␈α∩and␈α⊃3,␈α⊃with␈α∩exponents␈α⊃determined␈α⊃by␈α∩n.␈α⊃ We␈α∩also␈α⊃show
␈↓ α∧␈↓constructively␈α∪that␈α∀NOHO-graphs␈α∪are␈α∀planar␈α∪and␈α∀Hamiltonian,␈α∪and␈α∀we␈α∪mention
␈↓ α∧␈↓applications to related problems.
␈↓"β␈↓ α∧␈↓No. of pages:  61
␈↓"β␈↓ α∧␈↓Cost:  $ 3.45
␈↓"β␈↓ α∧␈↓--------------------------------------------------------------------------
␈↓"β␈↓ α∧␈↓STAN-CS-79-694  COMPUTER SCIENCE AT STANFORD, 1977-1978
␈↓"β␈↓ α∧␈↓Editor:  Jonathan King

␈↓"β␈↓ α∧␈↓    Abstract:␈α! This␈α!report␈α is␈α!a␈α!review␈α of␈α!Stanford␈α!Computer␈α Science
␈↓ α∧␈↓Department␈α)activities␈α)for␈α)the␈α)academic␈α)year␈α)1977-78.␈α) The␈α)report
␈↓ α∧␈↓includes:  ␈α~(1)␈α~The␈α~Chairman's␈α~overview␈α~of␈α~the␈α~important␈α~events␈α~of␈α~the
␈↓ α∧␈↓year,␈α∃(2)␈α∃Recent␈α∃activities␈α∃and␈α∃interests␈α∃of␈α∃faculty␈α∃members␈α∃and␈α∀research
␈↓ α∧␈↓associates␈α⊗arranged␈α⊗by␈α⊗research␈α⊗specialty,␈α⊗(3)␈α⊗Advanced␈α⊗doctoral␈α∃students
␈↓ α∧␈↓in␈α_each␈α↔specialty␈α_and␈α_their␈α↔research␈α_topics,␈α_(4)␈α↔Recipients␈α_of␈α_M.S.␈α↔and
␈↓ α∧␈↓Ph.D.␈α≥degrees,␈α≡(5)␈α≥Speakers␈α≡at␈α≥seminar␈α≥and␈α≡colloquia␈α≥series,␈α≡and␈α≥(6)
␈↓ α∧␈↓Bibliography of Computer Science Department technical reports.
␈↓"β␈↓ α∧␈↓No. of pages:  27
␈↓"β␈↓ α∧␈↓Cost:  $ 2.50
␈↓"β␈↓ α∧␈↓--------------------------------------------------------------------------
␈↓"β␈↓ α∧␈↓AIM-321  RECENT RESEARCH IN ARTIFICIAL INTELLIGENCE AND FOUNDATIONS
␈↓"β␈↓ α∧␈↓         OF PROGRAMMING
␈↓"β␈↓ α∧␈↓Authors:  Lester Earnest et al.

␈↓"β␈↓ α∧␈↓    Abstract:␈α* Summarizes␈α*recent␈α*research␈α*in␈α*the␈α*following␈α*areas:
␈↓ α∧␈↓artificial␈α#intelligence␈α#and␈α"formal␈α#reasoning,␈α#mathematical␈α#theory␈α"of
␈↓ α∧␈↓computation␈α7and␈α7program␈α6synthesis,␈α7program␈α7verification,␈α6image
␈↓ α∧␈↓understanding, and knowledge based programming.
␈↓"β␈↓ α∧␈↓No. of pages:  94
␈↓"β␈↓ α∧␈↓Cost:  $ 4.35
␈↓"β␈↓ α∧␈↓--------------------------------------------------------------------------
␈↓"β␈↓ α∧␈↓HPP-78-22  CONSIDERATIONS FOR MICROPROCESSOR-BASED TERMINAL DESIGN
␈↓"β␈↓ α∧␈↓Authors:  Reid G. Smith & Tom M. Mitchell

␈↓"β␈↓ α∧␈↓    Abstract:␈α$ We␈α%discuss␈α$the␈α%design␈α$of␈α%hardware␈α$and␈α%software␈α$for
␈↓ α∧␈↓inexpensive␈α∨microprocessorr-based␈α∨terminal/microcomputers.␈α∨ Such␈α∨devices
␈↓ α∧␈↓are␈α⊗fundamentally␈α⊗microcomputers␈α⊗that␈α⊗have␈α⊗been␈α⊗adapted,␈α⊗with␈α∃specialized
␈↓ α∧␈↓software, to operate as remote terminals for a host compuer.

␈↓"β␈↓ α∧␈↓    The␈α∨discussion␈α∨centers␈α∨on␈α≡a␈α∨specific␈α∨video␈α∨terminal␈α∨designed␈α≡and
␈↓ α∧␈↓constructed␈α≠by␈α≠the␈α~authors.␈α≠ This␈α≠terminal␈α≠is␈α~based␈α≠on␈α≠the␈α≠INTEL␈α~8080
␈↓ α∧␈↓microprocessor␈α≠and␈α≠is␈α≠equipped␈α≠with␈α≠software␈α≠sufficient␈α≠to␈α≠emulate␈α≠the
␈↓ α∧␈↓characteristics␈α⊗of␈α⊗standard␈α⊗video␈α⊗terminals␈α⊗required␈α⊗by␈α⊗several␈α∃available
␈↓ α∧␈↓SCREEN-ORIENTED text editors in common use at sites throughout the ARPAnet.

␈↓"β␈↓ α∧␈↓    We␈α#have␈α"found␈α#that␈α"the␈α#microprocessor␈α"adequately␈α#serves␈α#as␈α"the
␈↓ α∧␈↓controller␈α↔for␈α⊗such␈α↔terminals,␈α↔and␈α⊗that␈α↔a␈α⊗SOFTWARE-BASED␈α↔approach␈α↔to␈α⊗the
␈↓ α∧␈↓design␈α~of␈α~such␈α~terminals␈α~offers␈α~substantial␈α~advantages␈α≠in␈α~capabilities,
␈↓ α∧␈↓January␈↓ ε≡1979 Reports␈↓ s4

␈↓"β␈↓ α∧␈↓flexibility,␈α#and␈α"cost␈α#over␈α#the␈α"HARDWARE-BASED␈α#approach.␈α# We␈α"suggest
␈↓ α∧␈↓guidelines␈α≤for␈α≤future␈α≥designs␈α≤of␈α≤microprocessor-based␈α≤terminals␈α≥on␈α≤the
␈↓ α∧␈↓basis of our experience designing and using the terminal described here.

␈↓"β␈↓ α∧␈↓In␈α(order␈α'to␈α(take␈α(full␈α'advantage␈α(of␈α'the␈α(flexibility␈α(afforded␈α'by
␈↓ α∧␈↓microprocessor-based␈α%designs,␈α%we␈α%have␈α%implemented␈α%the␈α&capability␈α%to
␈↓ α∧␈↓DOWNLOAD␈α!and␈α!execute␈α!8080␈α!programs␈α written␈α!and␈α!assembled␈α!on␈α!a␈α host
␈↓ α∧␈↓computer.␈α∃ This␈α∃allows␈α∃the␈α∃user␈α∃to␈α∃customize␈α∃and␈α∃extend␈α∃the␈α∀microcomputer
␈↓ α∧␈↓with␈α∃the␈α∀software␈α∃development␈α∀tools␈α∃and␈α∀mass␈α∃storage␈α∀provided␈α∃by␈α∃the␈α∀host
␈↓ α∧␈↓computer.␈α∩ The␈α⊃terminal␈α∩is␈α⊃thus␈α∩a␈α⊃complete,␈α∩stan-alone␈α∩microcomputer␈α⊃system
␈↓ α∧␈↓specially configured for its role as a terminal.
␈↓"β␈↓ α∧␈↓No. of pages:  14
␈↓"β␈↓ α∧␈↓Cost:  $ 2.10
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␈↓"β␈↓ α∧␈↓␈↓ ε
Available from
␈↓"β␈↓ α∧␈↓␈↓ ∧0Stanford Systems Optimization Laboratory

␈↓"β␈↓ α∧␈↓SOL 78-19  A BIDIAGONALIZATION ALGORITHM FOR SPARSE LINEAR EQUATIONS AND
␈↓"β␈↓ α∧␈↓           LEAST-SQUARES PROBLEMS
␈↓"β␈↓ α∧␈↓Authors:  Christopher C. Paige & Michael A. Saunders

␈↓"β␈↓ α∧␈↓    Abstract:␈α∪ A␈α∪method␈α∪is␈α∪given␈α∪for␈α∩solving␈α∪Ax␈α∪=␈α∪b␈α∪and␈α∪min||Ax-b||␈↓#v2␈↓#␈α∩where
␈↓ α∧␈↓the␈α%matrix␈α%A␈α&is␈α%large␈α%and␈α%sparse.␈α& The␈α%method␈α%is␈α%based␈α&on␈α%the
␈↓ α∧␈↓bidiagonalization␈α#procedure␈α"of␈α#Golub␈α#and␈α"Kahan.␈α# It␈α#is␈α"analytically
␈↓ α∧␈↓equivalent␈α_to␈α_the␈α→method␈α_of␈α_conjugate␈α→gradients␈α_(CG)␈α_but␈α→possesses␈α_more
␈↓ α∧␈↓favorable␈α⊗numerical␈α⊗properties.␈α⊗ The␈α⊗Fortran␈α⊗implementation␈α⊗of␈α⊗the␈α∃method
␈↓ α∧␈↓(subroutine␈α≡LSQR)␈α≡incorporates␈α≡reliable␈α≡stopping␈α≡criteria␈α≡and␈α≥provides
␈↓ α∧␈↓estimates␈α_of␈α_various␈α→quantities␈α_including␈α_standard␈α→errors␈α_for␈α_x␈α→and␈α_the
␈↓ α∧␈↓condition␈α∃number␈α∃of␈α∃A.␈α∃ Numerical␈α∃tests␈α∃are␈α∃described␈α∃comparing␈α∃LSQR␈α∀with
␈↓ α∧␈↓several␈α∩other␈α⊃CG␈α∩algorithms.␈α⊃ Further␈α∩results␈α⊃for␈α∩a␈α⊃large␈α∩practical␈α⊃problem
␈↓ α∧␈↓illustrate␈α_the␈α_effect␈α_of␈α_pre-conditioning␈α_least-squares␈α_problems␈α_using␈α_a
␈↓ α∧␈↓sparse LU factorization of A.

␈↓"β␈↓ α∧␈↓Available␈α≠by␈α≠writing␈α≠directly␈α≠to:␈α≠ Gail␈α≠L.␈α≠Stein,␈α≠Systems␈α≠Optimization
␈↓ α∧␈↓Laboratory,␈α)Department␈α(of␈α)Operations␈α(Research,␈α)Stanford␈α(University,
␈↓ α∧␈↓Stanford, California 94305 U.S.A.
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