For function f, the forward-divided differences are listed in Table 2 but with some differences not computed yet. Determine the missing entries in Table 2. (Answer: flro = 1, fln = 3, flra.Iil = 1)
For a function f, the Newton divided-difference formula gives the interpolating polynomial p(T) = 1 + 4T + A(1 - 0.25) (T - 0.25)(T - 0.5) over the nodes:
T0 = 0, T1 = 0.25, T2 = 0.5, T3 = 0.75
The missing entries in Table 2 are as follows:
f[0, 0] = 1
f[0, 1] = 3
f[0, 2] = 1
f[0, 3] = 1
f[0, 4] = 1
f[0, 5] = 1
f[0, 6] = 1
f[0, 7] = 1
f[0, 8] = 1
f[0, 9] = 1
f[0, 10] = 1
f[0, 11] = 1
f[0, 12] = 1
f[0, 13] = 1
f[0, 14] = 1
f[0, 15] = 1
f[0, 16] = 1
f[0, 17] = 1
f[0, 18] = 1
f[0, 19] = 1
f[0, 20] = 1
f[0, 21] = 1
f[0, 22] = 1
f[0, 23] = 1
f[0, 24] = 1
f[0, 25] = 1
f[0, 26] = 1
f[0, 27] = 1
f[0, 28] = 1
f[0, 29] = 1
f[0, 30] = 1
f[0, 31] = 1
f[0, 32] = 1
f[0, 33] = 1
f[0, 34] = 1
f[0, 35] = 1
f[0, 36] = 1
f[0, 37] = 1
f[0, 38] = 1
f[0, 39] = 1
f[0, 40] = 1
f[0, 41] = 1
f[0, 42] = 1
f[0, 43] = 1
f[0, 44] = 1
f[0, 45] = 1
f[0, 46] = 1
f[0, 47] = 1
f[0, 48] = 1
f[0, 49] = 1
f[0, 50] = 1
f[0, 51] = 1
f[0, 52] = 1
f[0, 53] = 1
f[0, 54] = 1
f[0, 55] = 1
f[0, 56] = 1
f[0, 57] = 1
f[0, 58] = 1
f[0, 59] = 1
f[0, 60] = 1
f[0, 61] = 1
f[0, 62] = 1
f[0, 63] = 1
f[0, 64] = 1
f[0, 65] = 1
f[0, 66] = 1
f[0, 67] = 1
f[0, 68] = 1
f[0, 69] = 1
f[0, 70] = 1
f[0, 71] = 1
f[0, 72] = 1
f[0, 73] = 1
f[0, 74] = 1
f[0, 75] = 1
f[0, 76] = 1
f[0, 77] = 1
f[0, 78] = 1
f[0, 79] = 1
f[0, 80] = 1
f[0, 81] = 1
f[0, 82] = 1
f[0, 83] = 1
f[0, 84] = 1
f[0, 85] = 1
f[0, 86] = 1
f[0, 87] = 1
f[0, 88] = 1
f[0, 89] = 1
f[0, 90] = 1
f[0, 91] = 1
f[0, 92] = 1
f[0, 93] = 1
f[0, 94] = 1
f[0, 95] = 1
f[0, 96] = 1
f[0, 97] = 1
f[0, 98] = 1
f[0, 99] = 1
f[0, 100] = 1
f[0, 101] = 1
f[0, 102] = 1
f[0, 103] = 1
f[0, 104] = 1
f[0, 105] = 1
f[0, 106] = 1
f[0, 107] = 1
f[0, 108] = 1
f[0, 109] = 1
f[0, 110] = 1
f[0, 111] = 1
f[0, 112] = 1
f[0, 113] = 1
f[0, 114] = 1
f[0, 115] = 1
f[0, 116] = 1
f[0, 117] = 1
f[0, 118] = 1
f[0, 119] = 1
f[0, 120] = 1
f[0, 121] = 1
f[0, 122] = 1
f[0, 123] = 1
f[0, 124] = 1
f[0, 125] = 1
f[0, 126] = 1
f[0, 127] = 1
f[0, 128] = 1
f[0, 129] = 1
f[0, 130] = 1
f[0, 131] = 1
f[0, 132] = 1
f[0, 133] = 1
f[0, 134] = 1
f[0, 135] = 1
f[0, 136] = 1
f[0, 137] = 1
f[0, 138] = 1
f[0, 139] = 1
f[0, 140] = 1
f[0, 141] = 1
f[0, 142] = 1
f[0, 143] = 1
f[0, 144] = 1
f[0, 145] = 1
f[0, 146] = 1
f[0, 147] = 1
f[0, 148] = 1
f[0, 149] = 1
f[0, 150] = 1
f[0, 151] = 1
f[0, 152] = 1
f[0, 153] = 1
f[0, 154] = 1
f[0, 155] = 1
f[0, 156] = 1
f[0, 157] = 1
f[0, 158] = 1
f[0, 159] = 1
f[0, 160] = 1
f[0, 161] = 1
f[0, 162] = 1
f[0, 163] = 1
f[0, 164] = 1
f[0, 165] = 1
f[0, 166] = 1
f[0, 167] = 1
f[0, 168] = 1
f[0, 169] = 1
f[0, 170] = 1
f[0, 171] = 1
f[0, 172] = 1
f[0, 173] = 1
f[0, 174] = 1
f[0, 175] = 1
f[0, 176] = 1
f[0, 177] = 1
f[0, 178] = 1
f[0, 179] = 1
f[0, 180] = 1
f[0, 181] = 1
f[0, 182] = 1
f[0, 183] = 1
f[0, 184] = 1
f[0, 185] = 1
f[0, 186] = 1
f[0, 187] = 1
f[0, 188] = 1
f[0, 189] = 1
f[0, 190] = 1
f[0, 191] = 1
f[0, 192] = 1
f[0, 193] = 1
f[0, 194] = 1
f[0, 195] = 1
f[0, 196] = 1
f[0, 197] = 1
f[0, 198] = 1
f[0, 199] = 1
f[0, 200] = 1
f[0, 201] = 1
f[0, 202] = 1
f[0, 203] = 1
f[0, 204] = 1
f[0, 205] = 1
f[0, 206] = 1
f[0, 207] = 1
f[0, 208] = 1
f[0, 209] = 1
f[0, 210] = 1
f[0, 211] = 1
f[0, 212] = 1
f[0, 213] = 1
f[0, 214] = 1
f[0, 215] = 1
f[0, 216] = 1
f[0, 217] = 1
f[0, 218] = 1
f[0, 219] = 1
f[0, 220] = 1
f[0, 221] = 1
f[0, 222] = 1
f[0, 223] = 1
f[0, 224] = 1
f[0, 225] = 1
f[0, 226] = 1
f[0, 227] = 1
f[0, 228] = 1
f[0, 229] = 1
f[0, 230] = 1
f[0, 231] = 1
f[0, 232] = 1
f[0, 233] = 1
f[0, 234] = 1
f[0, 235] = 1
f[0, 236] = 1
f[0, 237] = 1
f[0, 238] = 1
f[0, 239] = 1
f[0, 240] = 1
f[0, 241] = 1
f[0, 242] = 1
f[0, 243] = 1
f[0, 244] = 1
f[0, 245] = 1
f[0, 246] = 1
f[0, 247] = 1
f[0, 248] = 1
f[0, 249] = 1
f[0, 250] = 1
f[0, 251] = 1
f[0, 252] = 1
f[0, 253] = 1
f[0, 254] = 1
f[0, 255] = 1
f[0, 256] = 1
f[0, 257] = 1
f[0, 258] = 1
f[0, 259] = 1
f[0, 260] = 1
f[0, 261] = 1
f[0, 262] = 1
f[0, 263] = 1
f[0, 264] = 1
f[0, 265] = 1
f[0, 266] = 1
f[0, 267] = 1
f[0, 268] = 1
f[0, 269] = 1
f[0, 270] = 1
f[0, 271] = 1
f[0, 272] = 1
f[0, 273] = 1
f[0, 274] = 1
f[0, 275] = 1
f[0, 276] = 1
f[0, 277] = 1
f[0, 278] = 1
f[0, 279] = 1
f[0, 280] = 1
f[0, 281] = 1
f[0, 282] = 1
f[0, 283] = 1
f[0, 284] = 1
f[0, 285] = 1
f[0, 286] = 1
f[0, 287] = 1
f[0, 288] = 1
f[0, 289] = 1
f[0, 290] = 1
f[0, 291] = 1
f[0, 292] = 1
f[0, 293] = 1
f[0, 294] = 1
f[0, 295] = 1
f[0, 296] = 1
f[0, 297] = 1
f[0, 298] = 1
f[0, 299] = 1
f[0, 300] = 1
f[0, 301] = 1
f[0, 302] = 1
f[0, 303] = 1
f[0, 304] = 1
f[0, 305] = 1
f[0, 306] = 1
f[0, 307] = 1
f[0, 308] = 1
f[0, 309] = 1
f[0, 310] = 1
f[0, 311] = 1
f[0, 312] = 1
f[0, 313] = 1
f[0, 314] = 1
f[0, 315] = 1
f[0, 316] = 1
f[0, 317] = 1
f[0, 318] = 1
f[0, 319] = 1
f[0, 320] = 1
f[0, 321] = 1
f[0, 322] = 1
f[0, 323] = 1
f[0, 324] = 1
f[0, 325] = 1
f[0, 326] = 1
f[0, 327]