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Internet Message Format  |  1995-03-31  |  13KB
  1. From: William C Wickes <billw@hpcvra.cv.hp.com>
  2. Subject:  v03i016:  proot - Polynomial Rootfinder v1.0, Part01/01
  3. Newsgroups: comp.sources.hp48
  4. Organization: Hewlett-Packard Co., Corvallis, OR, USA
  5. Followup-To: comp.sys.hp48
  6. Approved: spell@seq.uncwil.edu
  7.  
  8. Checksum: 2661449879 (verify with brik -cv)
  9. Submitted-by: William C Wickes <billw@hpcvra.cv.hp.com>
  10. Posting-number: Volume 3, Issue 16
  11. Archive-name: proot/part01
  12.  
  13.  
  14. BEGIN_DOC proot.doc
  15.               HP 48 Polynomial Rootfinder, for Real Coefficients
  16.  
  17. The HP 48 object listed below in ->ASC form is a high-performance polynomial
  18. root finder.  Those of you who remember the HP 71B Math Pac will recognize
  19. this as the same as the PROOT command from that Pac; it is in fact the same
  20. assembly-language code, given an RPL front end to operate in the HP 48.
  21. I will refer to the object as PROOT; you can, of course, give it any
  22. name you please by storing it in a global variable.
  23.  
  24. PROOT takes a (real) vector of coefficients in descending order, and returns
  25. a complex vector containing the polynomial roots:
  26.  
  27.              [ An An-1 An-2 ... A0 ] PROOT -> [ R1 R2 ... Rn ]
  28.  
  29. represents the determination of the n (complex) zeros R1 ... Rn of the
  30. nth-order polynomial
  31.  
  32.                     An x^n + An-1 x^n-1 + ... + A0
  33.  
  34. There is no limit on n, other than available memory and execution time.
  35. The coefficients Ai must be real numbers, but this limitation is at least
  36. partially compensated for by the speed and accuracy of the algorithm.  Also,
  37. no initial guess or stopping criterion is required.  PROOT uses
  38. Laguerre's method for n>2, or the quadratic or linear formulas for n<=2.
  39. You are referred to the HP 71 Math Pac Owner's Manual for more information.
  40.  
  41. The use of vectors rather than lists for the input and output derives from
  42. PROOT's HP71 origins.  You can easily add list/vector conversion around
  43. this object to make a more versatile version.  To be more fully compliant
  44. with HP 48 style you can write user-language programs to extract the
  45. polynomial coefficients from an arbitrary expression to use as a preliminary
  46. to PROOT, and to convert the result elements back into a factored expression
  47. (x-R1)(x-R2)...(x-Rn).  Examples of such programs are listed in
  48. HP 48 Insights Part II (if you'll excuse the plug).
  49.  
  50. Enjoy.
  51.  
  52. Bill Wickes
  53. HP Corvallis Division
  54. END_DOC
  55.  
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  211. M,@.EK]AAOG+W>S9\6WGI?SY\;W_?>T",O^@K9YCWK2>4IY=FK7?J,=0R(`?L\
  212. M^A*``3D@![\WJNQ5#W$Y>^X*=8!S@1_!,15T0.P!ZG:MK@Q0]X_GN\IRWHB/5
  213. MJ`P1RAZ@]0V%!@:7CP)#$P#@>@.,7HA_QXW>A(]_ZBLGH(6`['T?P3$5EU%'.
  214. M2?IQ2HU^AH\N@G_360C(.?:'!,>HY['H)OAGIA>B5ROHYO?XI[Z"[H*/WH%__
  215. MCYG1",AI]\A^\)?(MY['F?>=U^3'OW>;5Z2'K/B+O@)U[XG>@+_,^+"W<NMY`
  216. MP8F^>H]_>BL"(U!PI8D^>8_.>X_^?7^3>9AP*7F9?&QYBXV^=7^^#(5_>BOHU
  217. M9/?H:?<WV^>7EY'7''$?1P>@Z"+W][L7DE#W&D>VYY]0)QSH'/?H._?HE/W'!
  218. MQ.C_]H>'!8!.;F^N>6)\Y'A,>=QX"8DNC(]>AW\T>;1XUWS$<#N)CH1_ZWB:'
  219. MB-Z$?[>,/H2/3H=_CWRB$/9AA&Z!?\6(;H9_>H!>@8^^:8\N@(_^:(].9J]L$
  220. MQXWH)_A):G!&<#F,WGV/OH:/CH%_AHQ^AH^.?G^`B.Y_CYY[?V:,OH./S'R_H
  221. MS!&X[`$(@1Y=CPYX?_QX7I#7!M;%Z-#URH(N78^^8']=<#V,;E\?^(%TE(A.]
  222. M5H^>71^A20H1@<H6@,H`@>QQ+QZ1&7Z@#!`9O8`N55_O=P#8#[J"?EB/;FZ/B
  223. FOE>/S%0_D:$?>@7$!%4%>Z7FU2ZEPSN$41E]OU_:I`P0*S&P$@.PS
  224. ``
  225. end
  226. END_UU
  227.