{"text_format":"1","workbook":"xlsx","n_sheets":1,"sheets":["Bisection Method"],"not_rendered":{"charts":0,"images":1,"macros":1,"external_links":0,"defined_names":0,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Bisection Method","index":0,"n_rows":30,"n_cols":17,"rows_kept":30,"cut":false,"hidden":false,"merged":[[15,14,15,15],[18,14,18,15],[15,16,15,20],[18,16,18,20],[21,14,21,15],[21,16,21,20],[9,4,9,12],[10,4,10,12],[2,4,2,12],[4,4,4,12],[5,4,5,12],[6,4,6,12],[7,4,7,12],[8,4,8,12]]}
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"www.numerical-methods.com"]
[null,null,null,null,"Bisection Method"]
[]
[null,null,null,null,"The bisection method is a .method for finding the root or solution of an equation."]
[null,null,null,null,"In this demonstration the function f(x) is defined as a macro. "]
[null,null,null,null,"The function f(x) can be edited by typing <Alt><F11>. An image of the macro screen is shown."]
[null,null,null,null,"Initially the root has to be located within an interval, denoted [a,b] and their values are placed in the yellow cells."]
[null,null,null,null,"In this demonstration f(x)=x^3-20 and the interval is [2,3}."]
[null,null,null,null,"In the bisection method the interval or bracket [a,b] is halved in size at each iteration. "]
[null,null,null,null,"Each line shows an iteration. The columns headed 'a' and 'b' show the bracket and the root is at the bottom."]
[]
[null,null,null,null,"a","b",null,"f(a)","f(b)",null,"mid-point",null,"f(mid-point)"]
[null,null,null,null,2,3,null,{"$f":"f(E14)","v":-12},{"$f":"f(F14)","v":7},null,{"$f":"(E14+F14)/2","v":2.5},null,{"$f":"f(K14)","v":-4.375}]
[null,null,null,null,{"$f":"IF(H14*M14>0,K14,E14)","v":2.5},{"$f":"IF(I14*M14>0,K14,F14)","v":3},null,{"$f":"f(E15)","v":-4.375},{"$f":"f(F15)","v":7},null,{"$f":"(E15+F15)/2","v":2.75},null,{"$f":"f(K15)","v":0.796875}]
[null,null,null,null,{"$f":"IF(H15*M15>0,K15,E15)","v":2.5},{"$f":"IF(I15*M15>0,K15,F15)","v":2.75},null,-4.375,0.796875,null,{"$f":"(E16+F16)/2","v":2.625},null,-1.912109375,null,"User Guide",null,"Bisection Method.pdf"]
[null,null,null,null,2.625,2.75,null,-1.912109375,0.796875,null,2.6875,null,-0.589111328125]
[null,null,null,null,2.6875,2.75,null,-0.589111328125,0.796875,null,2.71875,null,9.5916748046875E-2]
[null,null,null,null,2.6875,2.71875,null,-0.589111328125,9.5916748046875E-2,null,2.703125,null,-0.24857711791992188,null,"User Group",null,"Spreadsheets in Science and Technology"]
[null,null,null,null,2.703125,2.71875,null,-0.24857711791992188,9.5916748046875E-2,null,2.7109375,null,-7.6826572418212891E-2]
[null,null,null,null,2.7109375,2.71875,null,-7.6826572418212891E-2,9.5916748046875E-2,null,2.71484375,null,9.4208121299743652E-3]
[null,null,null,null,2.7109375,2.71484375,null,-7.6826572418212891E-2,9.4208121299743652E-3,null,2.712890625,null,-3.3733926713466644E-2,null,"Web source",null,"Bisection Method.xlsm"]
[null,null,null,null,2.712890625,2.71484375,null,-3.3733926713466644E-2,9.4208121299743652E-3,null,2.7138671875,null,-1.2164321728050709E-2]
[null,null,null,null,2.7138671875,2.71484375,null,-1.2164321728050709E-2,9.4208121299743652E-3,null,2.71435546875,null,-1.3736962573602796E-3]
[null,null,null,null,2.71435546875,2.71484375,null,-1.3736962573602796E-3,9.4208121299743652E-3,null,2.714599609375,null,4.0230725280707702E-3]
[null,null,null,null,{"$f":"IF(H25*M25>0,K25,E25)","v":2.71435546875},{"$f":"IF(I25*M25>0,K25,F25)","v":2.714599609375},null,-1.3736962573602796E-3,4.0230725280707702E-3,null,{"$f":"(E26+F26)/2","v":2.7144775390625},null,1.3245667887531454E-3]
[null,null,null,null,2.71435546875,2.7144775390625,null,-1.3736962573602796E-3,1.3245667887531454E-3,null,2.71441650390625,null,-2.4595070271971053E-5]
[null,null,null,null,2.71441650390625,2.7144775390625,null,-2.4595070271971053E-5,1.3245667887531454E-3,null,2.714447021484375,null,6.4997827516322104E-4]
[null,null,null,null,2.71441650390625,2.714447021484375,null,-2.4595070271971053E-5,6.4997827516322104E-4,null,2.7144317626953125,null,3.1268970643694161E-4]
[null,null,null,null,2.71441650390625,2.7144317626953125,null,-2.4595070271971053E-5,3.1268970643694161E-4,null,2.7144241333007813,null,1.4404684408120261E-4]